Do problem 1.4. 1.4 See Exercise 1.2. Among all policyholders who live within fi

Question

Do problem 1.4. 1.4 See Exercise 1.2. Among all policyholders who live within five miles of the Atlantic Ocean, 75% live in Florida, 20% live in Louisiana, and 5% live in Texas. For those who live close to the ocean the probabilities of filing a clainm increase, as given in Table 1.2. Assume that a policyholder lives within five miles of the Atlantic coast. Use the law of total probability for conditional probability in Exercise 1.3 to find the chance they will file a claim for flood damage next year

Explanation / Answer

Ans:

Given that

P(Florida)=0.75

P(Louisiana)=0.20

P(Texas)=0.05

Also,

P(claim/Florida)=0.03

P(claim/Louisiana)=0.015

P(claim/Texas)=0.02

Now,

P(claim)=P(claim/Florida)*P(Florida)+P(claim/Louisiana)*P(Louisiana)+P(claim/Texas)*P(Texas)

=0.03*0.75+0.015*0.20+0.02*0.05

=0.0265

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