Kilgallen Inc. has the total inventory of $1,000. Currently, Kilgallen has this entire inventory stored in one warehouse. There is a 10% chance that a fire could occur. If this fire occurs, then Kilgallen will lose their entire inventory. [Option A]
As an alternative to keeping their entire inventory in one warehouse, Kilgallen is considering separating their inventory evenly into two different warehouses. Once again, there is a 10% chance that a fire could occur in each warehouse. If this fire occurs, then Kilgallen would once again lose their entire inventory in that particular warehouse. [Option B]
a. Derive the probability distribution for total losses under Option A. Once again remember that if a fire occurs, the loss will be $1,000.
b. Derive the probability distribution for total losses under Option B. Hint: In the case of Option B, you need to consider all the possible outcomes, recognizing that Kilgallen now has two warehouses.
c. Compare the amount of risk Kilgallen faces under Option A vs. Option B. Which option has more risk? Justify and demonstrate your answer.