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Question 1 of 30
1. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 2 of 30
2. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 3 of 30
3. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 4 of 30
4. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 5 of 30
5. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 6 of 30
6. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 7 of 30
7. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 8 of 30
8. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 9 of 30
9. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 10 of 30
10. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 11 of 30
11. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 12 of 30
12. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 13 of 30
13. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 14 of 30
14. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 15 of 30
15. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 16 of 30
16. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 17 of 30
17. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 18 of 30
18. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 19 of 30
19. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 20 of 30
20. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 21 of 30
21. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 22 of 30
22. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 23 of 30
23. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 24 of 30
24. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 25 of 30
25. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 26 of 30
26. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 27 of 30
27. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 28 of 30
28. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 29 of 30
29. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
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Question 30 of 30
30. Question
Question: In a commercial building, an alarm system is designed to detect unauthorized access through multiple entry points. The system is programmed to trigger an alarm if it detects motion in a restricted area for more than 30 seconds. If the alarm is triggered, it sends a notification to the security personnel and initiates a lockdown procedure. If the motion sensor detects movement for 15 seconds, then there is a 50% chance of false alarm, while for 30 seconds, the chance of a false alarm drops to 10%. If the alarm is triggered, what is the probability that it was a true alarm given that the motion was detected for 30 seconds?
Correct
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.
Incorrect
We know the following: – The probability of a false alarm after 30 seconds is 10%, which means the probability of a true alarm is \( P(A|B) = 1 – P(\text{False Alarm}|B) = 1 – 0.1 = 0.9 \) or 90%. – The probability of a false alarm after 15 seconds is 50%, but this does not affect our calculation for the 30-second scenario. Thus, when the alarm is triggered after 30 seconds of motion detection, the likelihood that it is a true alarm is significantly higher due to the reduced chance of a false alarm. In conclusion, the probability that the alarm was a true alarm given that motion was detected for 30 seconds is 90%. This scenario emphasizes the importance of understanding how alarm systems are designed to minimize false alarms and the critical role of timing in assessing alarm validity. Properly configured alarm systems can significantly enhance security measures by ensuring that responses are based on reliable data, thereby allowing security personnel to act effectively and efficiently in real situations.