Question

​David, the promoter of an outdoor​ concert, expects a net profit of​ $100,000, unless it​ rains, which would reduce the net profit to ​$40 comma 000. The probability of rain is 0.20. For a premium of ​$25 comma 000 David can purchase insurance coverage that would pay him​ $100,000 in case of rain. Based on expected​ values, which is​ David's wiser choice in this​ situation?

Answer 1

David's wiser choice, based on the expected values, would be not to purchase the insurance as his expected profit without insurance is $88,000, which is higher than the expected profit of $83,000 with insurance.

Step-by-step explanation:

The question poses a scenario involving expected value calculation to determine the best financial decision for an outdoor concert promoter named David. We are to evaluate whether purchasing insurance for an outdoor concert, given a certain probability of rain, is a wise choice based on expected values.

If David does not purchase insurance, his expected profit would be:

(0.80)($100,000) + (0.20)($40,000) = $80,000 + $8,000 = $88,000.

If David does purchase the insurance for $25,000, his expected profit would be:

(0.80)($100,000 - $25,000) + (0.20)($140,000 - $25,000) = $60,000 + $23,000 = $83,000.

By comparing the two expected values, the higher expected profit is without purchasing the insurance, which is $88,000 versus $83,000 with insurance.

Answer 2

Not purchase insurance

Step-by-step explanation:

The probability of rain is 0.20

=> The probability of the not rain situation is: 1 - 0.2 = 0.8

If David does not buy the insurance, the expected net profit he would receive can be calculated as following:

Expected net profit = Probability of rain x Net profit when its rains + Probability of not rain x Net profit when it does not rain

= 0.20 x 40,000 + 0.8 x 100,000 = $88,000

If David buy the insurance:

+) When it does not rain: He will receive net profit of $100,000

+) When it rains: He will receive $40,000 as profit and $100,000 as insurance coverage

So that:

Expected net profit = Probability of rain x Net profit when its rains + Probability of not rain x Net profit when it does not rain - Insurance fee

= 0.2 x (40,000 + 100,000) + 0.8 x 100,000 - 25,000 = $83,000

As we can see, the expected net profit David receives when buying insurance is less than when he does not buy, so that he should not buy the insurance.