An automobile insurance company classifies each driver as a good risk, a medium

Question

An automobile insurance company classifies each driver as a good risk, a medium risk, or a bad risk. Of those currently insured, 30% are good risks, 50% are medium risks, and 20% are bad risks. In any given year, the probability of at least one citation is 0.1 for a good-risk driver, 0.3 for a medium-risk driver, and 0.5 for a bad-risk driver. (a) What proportion of drivers receive a citation during a particular year. (b) If a randomly selected driver is found to have at least one citation in a particular year, what is the probability that the driver is a good risk? (c) If a randomly selected driver is found to have no citations in a particular year, what is the probability that the driver is a bad risk?

Explanation / Answer

Ans:

a)Probability that driver recieve a citation=0.3*0.1+0.5*0.3+0.2*0.5

=0.03+0.15+0.1

=0.28

b)P(good risk/citation)=0.3*0.1/0.28=0.1071

c)P(bad risk/no citation)=0.5/(1-0.28)=0.5/0.72=0.694

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