Question

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 that 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?

Answer 1

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.