All insurance company divides its policy holders into three categories low risk,

Question

All insurance company divides its policy holders into three categories low risk, mode risk. and high risk. The low-risk policy holder's account for 60% of the total number of people insured the company. The moderate-risk policy holders account for 30%. and the high-risk policy holders account for 10%. The probabilities that a low-risk, moderste-rik. and high-risk policy holder will file a claim within a given year are respectively 0.01.0.10. and 0.50. What is the probability that a policy holder will file a claim this year? Given that a policy holder files a claim this year, what is the probability that the person is a low-risk policy holder?

Explanation / Answer

a) H=high

M=medium

L=low

P(H)=0.1

P(M)=0.3

P(L)=0.6

D: filing a claim

P(D/L)=0.01

P(D/M)=0.1

P(D/H)=0.5

P(D)=P(L)*P(D/L)+P(M)*P(D/M)+P(H)*P(D/H)=0.331

b)P(L/D)=P(D/L)P(L)/P(D)=0.01813

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