Question

1. 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? g

Answer 1

0.8675

Explanation:

Given that 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.

age 16-30 31-64 >65

Prob 0.15 0.8 0.05 1

Prob for accidents 0.06 0.09 0.04

Product 0.009 0.072 0.002 0.083

Prob for 31-64 causing it/accident =
`(0.072)/(0.083) \\=0.8675`

Using Bayes theorem we got answer as 0.8675