select the correct answer. acasa insurance company offers several plans for home insurance. • plan a has a…

select the correct answer. acasa insurance company offers several plans for home insurance. • plan a has a $700 yearly premium with a $3,000 deductible. • plan b has a $1,200 yearly premium with a $1,000 deductible. the average payout by the insurance company for a fire claim is $27,000. suppose 5% of the claims were for fire damage. what would acasas expected value (loss or gain) be per customer who chooses plan a? a. -$25,300 b. -$1,350 c. $850 d. -$500

select the correct answer. acasa insurance company offers several plans for home insurance. • plan a has a $700 yearly premium with a $3,000 deductible. • plan b has a $1,200 yearly premium with a $1,000 deductible. the average payout by the insurance company for a fire claim is $27,000. suppose 5% of the claims were for fire damage. what would acasas expected value (loss or gain) be per customer who chooses plan a? a. -$25,300 b. -$1,350 c. $850 d. -$500

Answer

Explanation:

Step1: Calculate gain when no fire - claim

The customer pays a premium of $700. The probability of no fire - claim is $1 - 0.05=0.95$. The gain for the insurance company in this case is the premium amount, so the contribution to the expected value is $700\times0.95$. $700\times0.95 = 665$

Step2: Calculate gain when there is a fire - claim

The customer pays a premium of $700$ and has a deductible of $3000$. The insurance company's payout for a fire - claim is $27000$. So the net cost to the insurance company for a fire - claim is $27000 - 3000=24000$. The gain for the insurance company in case of a fire - claim is $700-24000=- 23300$. The probability of a fire - claim is $0.05$. So the contribution to the expected value is $(-23300)\times0.05$. $(-23300)\times0.05=-1165$

Step3: Calculate the expected value

The expected value $E$ is the sum of the contributions from no - fire and fire - claim cases. $E=665+( - 1165)$ $E=-500$

Answer:

D. -$500$