1. Consider the following two scenarios [Option A and Option B]:

Shepherd Inc. has a total of 150 computers. Currently, Shepherd Inc. has all 150 computers stored in one warehouse. There is a 20% chance that a fire could occur. If this fire occurs, then Shepherd will lose all 150 computers. [Option A]

Alternatively, Shepherd is considering separating their computers evenly into two different warehouses: 75 computers stored in Warehouse I and 75 computers stored in Warehouse II. Once again, there is a 20% chance that a fire could occur in each warehouse. If a fire occurs, then Shepherd would once again lose their entire computers in that particular warehouse. [Option B]

Read about this concept in Chapter 5 of your textbook under the heading Separation on pages 5.9 5.12 in order to answer this question properly.

1. First, consider Option A.

Derive the probability distribution for total number of lost computers under Option A. Hint: Think about the definition of a probability distribution and apply it in this case. [2 points]

2. Now consider Option B.

Derive the probability distribution for total number of lost computers under Option B. Hint: In the case of Option B, you need to consider all the possible outcomes in terms of number of lost computers, recognizing that Shepherd now has two warehouses. Further hint: consider the rules of probability as discussed in class when you derive your probability distribution. [3 points]

3. Compare the amount of risk Shepherd faces under Option A vs. Option B.

• What is the measure of risk? Hint: Recall our discussion in Topic 4. [1 point]

• Which option has more risk, Option A or Option B? Justify and demonstrate your answer. [2 points]