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?

Not purchase insurance

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.

answerthe above statement is false;