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.

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