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+. Furthermor

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

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Sarah 2 weeks 2021-11-22T02:41:11+00:00 1 Answer 0

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    2021-11-22T02:42:55+00:00

    Answer:

    0.8675

    Step-by-step 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 =\frac{0.072}{0.083} \\=0.8675

    Using Bayes theorem we got answer as 0.8675

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