106 The probability that a onecar accident is due to faulty

106. The probability that a one-car accident is due to faulty brakes is 0.04, the probability that a one-car accident is correctly attributed to faulty brakes is 0.82, and the probability that a one-car accident is incorrectly attributed to faulty brakes is 0.03. What is the probability that (a) a one-car accident will be attributed to faulty brakes; (b) a one-car accident attributed to faulty brakes was actually due to faulty brakes?

Solution

P(car accident due to faulty brakes) = 0.04

P(correctly attributed) = 0.82

P(non correctly attributed) = 0.03

P(car accident not due to faulty brakes) = 1 - P(car accident due to faulty brakes) = 1 - 0.04 = 0.96

P(accident due to faulty brakes| car accident is attributed due to faulty brakes)

= (0.04*0.82)/(0.04*82 + 0.96*0.03) = 0.5324