Problem 4: An automobile insurance company classifies each driver as a good risk

Question

Problem 4: An automobile insurance company classifies each driver as a good risk, a medium risk, or a poor risk. Of those currently insured, 30% are good risks, 50% are medium risks and 20% are poor risks. In any given year, the probability that a driver will have at least one citation is 0.1 for a good risk, 0.3 for a medium risk, and 0.5 for a poor risk. (a) What is the probability that a randomly selected driver insured by this company has at b) If a randomly selected driver insured by this company has at least one citation during (c) If a randomly selected driver insured by this company does not have any citation during least one citation during the next year? the next year, what is the probability that the driver was actually a good risk? the next year, what is the probability that the driver was actually a good risk? Answer: Your answer here

Explanation / Answer

a)P(at least one citation)=P(good risk and at least one citation+medium risk and at least one citation+poor risk and at least one citation)=0.3*0.1+0.5*0.3+0.2*0.5=0.28

b)

P(good risk|at least one citation)=P(good risk and at least one citation)/P(at least one citation)

=0.3*0.1/0.28=0.1071

c)

P(not have any citation)=1-P(at least one citation)=1-0.28=0.72

hence P(good risk|not have any citation)=P(good risk and no citation)/P(no citation)

=0.3*(1-0.1)/0.72=0.3750

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