Assume that there are two business owners and each own an identical plant. The Business Owner A has a Plant A valued at $40,000 while the Business Owner B has a Plant B valued at $60,000. Moreover, it is assumed that there is a 20% chance in any year that each plant will be destroyed by a fire. In addition, a loss to either plant is an independent event.

a. Calculate the expected annual loss and the standard deviation for the expected annual loss for each owner.

Next, assume that instead of bearing the risk individually, the two business owners decide to pool their loss exposures. They agree to pay any loss that might occur based on the proportion to their plant value over the pool value. More specifically, the Business Owner A will agree to pay $40,000 / (40,000 + 60,000) = 40% of any loss that might occur in the pool. For the Business Owner B, the percentage to pay any loss in the pool is calculated in a similar way. Under this scenario;

b. Define the possible outcomes and their relevant probabilities.

c. Calculate the amount of loss for each business owner based on the possible outcomes.

d. Calculate the expected loss and the standard deviation of the expected loss for the Business Owner A and the Business Owner B, separately