Question

Suppose people ages 16-30 make up 15% of drivers on the road, 80% of drivers are aged 31-64, and 5% of drivers are aged 65+. Furthermore, suppose drivers in each age range cause car accidents at the rates of 6%, 4%, and 9%, respectively, Given an accident occurred, what is the probability a driver aged 31-64 caused it?

Please explain step by step how to go through this problem

Answer 1

P(16 - 30) = 0.15

P(31 - 64) = 0.80

P(65+) = 0.05

P(Accident | 16-30) = 0.06

P(Accident | 31-64) = 0.04

P(Accident | 65+) = 0.09

Hence by Bayes' theorem:

P(31-64 | Accident)

= 0.7033