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 $25,000. The probability of rain is 0.30. For a premium of$23,000 David can purchase insurance coverage that would pay him $100,000 in case of rain. Find the expected net profit when the insurance is not purchased.

Answer 1

We have to use the expected value formula, which is about the sum of multiplying each event by its probability.

$\begin{gathered} E=0.30\cdot25000+0.70\cdot100000=7500+70000 \\ E=77500 \end{gathered}$

Given that David didn't purchase the insurance, we don't have to include that information in the formula.

Therefore, the expected net profit is $77,500.