# risk and statistics 1

Consider the following two scenarios [Option A and Option B]: TabataInc. has the total inventory of $7,500. Currently, Tabatahas thisentire inventory stored in one warehouse. There is a 6% chance that a fire could occur. If this fire occurs, then Tabatawill lose their entire inventory.

[Option A] As an alternative to keeping their entire inventory in one warehouse, Tabatais considering separatingtheir inventory evenly into two different warehouses. Once again, there is a 6% chance that a fire could occur in each warehouse. If this fire occurs, then Tabatawould 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 â€˜Separationâ€™ on pages 5.9 â€“5.12 in order to answer this question properly.

a.First, consider Option A. What is the probability of having zero dollars in losses? What is the probability of having $7,500 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 â€“we did this in Topic 4.[2 points]

b.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 Tabata now has two warehouses. Further hint: consider the rules of probability as discussed in class when you derive your probability distribution. [4 points]

c.Compare the amount of riskTabatafaces under Option A vs. Option B. Which option has more risk? Justify and demonstrate your answer. Recall our discussion on standard deviation. [4 points]