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

Manaka Inc. has the total inventory of $6,000. Currently, Manaka has this entire inventory stored in one warehouse. There is a 20% chance that a fire could occur. If this fire occurs, then Manaka will **lose their entire inventory**. [Option A]

As an alternative to keeping their entire inventory in one warehouse, Manaka is considering **separating **their inventory **evenly into two different warehouses**. Once again, there is a 20% chance that a fire could occur in each warehouse. If this fire occurs, then Manaka would once again lose their entire inventory in **that particular warehouse**. [Option B]

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

1. First, consider **Option A**.

What is the probability of having zero dollars in losses? What is the probability of having $6,000 in losses?

Derive the **probability distribution for total dollar losses under Option A**. Note that this question asks for total dollar losses, not number of losses. 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 losses under Option B**. Hint: In the case of Option B, you need to consider all the possible outcomes in terms of dollar amount of losses, recognizing that Manaka now has two warehouses. Further hint: consider the rules of probability as discussed in class when you derive your probability distribution. [4 points]

3. Compare the **amount of risk **Manaka faces under Option A vs. Option B. Which option has more risk? Justify and demonstrate your answer. Recall our discussion in Topic 4 about how we measure risk. [4 points]

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