All insurance company divides its policy holders into three

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?

Solution

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