Question

1. Based on historical data for a fictitious airline, they experience a mechanical failure on 20% of their flights. Their crash rate for flights given a mechanical failure occurs is 60%, while their crash rate for flights given no mechanical failure occurs is 8%. Imagine an airplane operated by this airline crashes, what is the probability it had a mechanical failure?

Answer 1

Define event A - Airplane operated by the company crashes

event B - Airplane operated by company experiences mechanical failure. and 1-B= No mechanical failure is experienced.

Given P( A| B) = P( flight crashes given a mechanical failure occurs ) = 0.60 and

P (A| (1-B)) = P( flight crashes given no mechanical failure occurs ) = 0.08

Also the prior probability of mechanical failure = P(B) = 0.20

If an airplane operated by this airline crashes, the probability it had mechanical failure is = P( B |A)

By Bayes'' theorem,  

= 0.65 which is the required probability