On any night, there is a 92% chance that an burglary attempt will trigger the alarm, and a 1% chance of a false alarm, namely th

Question

2 years ago

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On any night, there is a 92% chance that an burglary attempt will trigger the alarm, and a 1% chance of a false alarm, namely th

at the alarm will go off when there is no burglary. The chance that a house will be burglarized on a given night is 1/1000 . What is the chance of a burglary attempt if you wake up at night to the sound of your alarm?

Mathematics

1 answer:

Semmy [17] · Answer 1 · 2023-08-14T03:09:57+03:00

Semmy [17]2 years ago

3 0

Answer:

Step-by-step explanation:

Step1: P(Burglary) = .001

Step2: P(Alarm|Burglary Happens) = .92

Step3: Probability of alarm going (in total) = P(Alarm) when burglary happens + P(Alarm) when burglary does not happen.

Step4: Use Bayes theorem.