Capital Goods, Inc. has total inventory of $1,000. Capital Goods has the entire

Question

Capital Goods, Inc. has total inventory of $1,000. Capital Goods has the entire inventory stored in one warehouse. There is a 3% chance that a fire could occur in the warehouse. If this fire occurs, then Capital Goods will lose their entire inventory. (Option A)

As an alternative to keeping all of their inventory in one warehouse, Capital Goods is considering separating their inventory evenly into two different warehouses. Once again, there is a 3% chance that a fire could occur in any one warehouse. If this fire occurs, then Capital Goods will lose their inventory in that particular warehouse. (Option B)

1. Derive the probability distribution for total losses under Option A. Once again, remember that if a fire occurs, the loss will be $1,000. Hint: Think about the definition of a probability distribution and apply it in this case. (4 points)

2. Derive the probability distribution for total loses under Option B. Hint: In the case of Option B, you need to consider all possible outcomes, recognizing that Capital Goods now has two warehouses. Consider the rules of probability as discussed in class when you derive your probability distribution. (10 points)

3. Compare the amount of risk Capital Goods faces under Option A vs. Option B. Which option has more risk? Why? Show all calculations. Explain your answer. (10 points)

Explanation / Answer

1.

P(X= fire) = 0.03 P(X=no fire) =0.97

Fire =1000 loss

no fire =0 loss

So,Expected losses = $1000*0.03 = $30

2.Probability distribution

X=1 if fire in first warehouse

X=0 fire not in first warehouse

Y=1 if fire in second warehouse

Y=0 no fire in second warehouse

P(X=0,Y=0) = 0.97^2

P(X=1,Y=0) = 0.03*0.97 = 0.0291

P(X=0,Y=1) = 0.97*0.03 = 0.0291

P(X=1,Y=1) = 0.03*0.03 = 0.0009

Expected loss = 500( 0.0291 + 0.0291) + 1000*0.0009 = 30

3. Rish is the same. But probabilities of both getting fired(0.97^2) is less than the probability of one getting fired in option A(0.97). But risk or expected loss remains the same

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