# Construct the probability distribution for total losses under Option B.

Now assume from past information, ELS has constructed the following probability distribution (PD) for the dollar amount of loss when accidents do occur. Hint: severity.

$ amount of losses Probability of dollar losses

2,000 .40

8,000 .35

15,000 .25

• Find the expected cost per accident, i.e., calculate the E(S). (3 points)

• Calculate the expected loss per vehicle per year. (3 points)

IOJK

• Calculate the expected loss for all vehicles per year. (3 points)

Consider the following two scenarios [Option A and Option B];

Butler, Inc. has total inventory of $200,000. Butler has this entire inventory stored in one warehouse. There is a 4% change that a fire could occur. If this fire occurs, then Butler will lose their entire inventory. [Option A]

As an alternative to keeping their entire inventory in one warehouse, Butler is considering separating their inventory evenly into two different warehouses. Once again, there is a 4% chance that a fire could occur in each warehouse. If this fire occurs, then Butler would once again lose their entire inventory in that particular warehouse. [Option B]

• Construct the probability distribution for total losses under Option A. Once again remember that if a fire occurs, the loss will be $200,000. Hint: Think about the definition of a probability distribution and apply it in this case. (4 points)

• Construct the probability distribution for total losses under Option B.o Hint: In the case of Option B, you need to consider all the possible outcomes, recognizing that Butler now has two warehouses. Further hint…. Consider the rules of probability as discussed in class when you derive your probability distribution. Show probabilities to 4 decimal places. (10 points)

• Compare the amount of risk Butler faces under Option A vs. Option B. Which option has more risk? Why? Show all of your work. And, explain your answer. (10 points)

• Hint: Measurement of Risk = Coefficient of Variation = Standard Deviation / Mean

Mean or EL = SUM of ($ amount of loss * Probability of that loss) each situation

Variance = SUM of [(Prob of Loss * ($ amt of that loss – EL)^2] each situation

SD = Square root of Variance