Question

An auto insurance company insures drivers of all ages. An actuary compiled the following statistics on the company’s insured drivers: Age of Driver Probability of Accident Portion of Company’s Insured Drivers 16-20 21-30 31-65 66-99 0.06 0.03 0.02 0.04 0.08 0.15 0.49 0.28 A randomly selected driver that the company insures has an accident. Calculate the probability that the driver was age 16-20.

Answer 1

Answer:

0.16

Step-by-step explanation:

You can use the Bayes theorem, it lets you calculate the probability of occurrence of an event knowing that others happened before and the probability of other events.

Labeling the events.

A= A driver has an accident

B,C,D,E= The driver´s age is between 16-20, 21-30, 31-65 and 66-99 respectively.

In this case the bayes theorem is :

$P(B|A)=\frac{P(A|B)P(B)}{P(A|B)P(B)+P(A|C)P(C)+P(A|D)P(D)+P(A|E)P(E)}$

The probabilities are:

P(B)= 0.08

P(C)=0.15

P(D)=0.49

P(E)=0.28

P(A|B)=0.06

P(A|C)=0.03

P(A|D)=0.02

P(A|E)=0.04

Calculating:

$P(B|A)=\frac{0.06*0.08}{0.06*0.08+0.03*0.15+0.02*0.49+0.04*0.28}=0.1584$

Aproximately 0.16