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 occurs, what is the probability a driver aged 31-64 caused it?

Accepted Solution

Answer: Our required probability is 0.05.Step-by-step explanation:Since we have given that Probability of drivers within ages 16-30 = 15%Probability of drivers within ages 31-64 = 80%Probability of drivers within ages 65+ = 5%Percentage of accidents in 16-30 ages = 6%Percentage of accidents in 31-64 ages = 4%Percentage of accidents in 65+ ages = 9%Given an accident occurs, probability a driver aged 31-64 caused it is given by[tex]\dfrac{4}{80}\\\\=\dfrac{1}{20}\\\\=0.05[/tex]Hence, our required probability is 0.05.