Consider the following two scenarios [Option A and Option B: Rachel\'s clothing
ID: 3328130 • Letter: C
Question
Consider the following two scenarios [Option A and Option B: Rachel's clothing boutique has one dry cleaning machine to press the new clothes. It is a very large machine; it has 10% chance in any one year of being destroyed. If it is destroyed, the machine will cost $5,000 to replace. (Option A) Rachel is considering selling the large machine and buying two smaller machines. A small machine would cost $2,500 to replace if it is destroyed, and it has a 10% chance of being destroyed. (Option B) Assuming the operation and cost of the two small machines is the same as the large machine. Which situation faces the most risk? It is not acceptable to just guess one or the other. Points will only be awarded for you demonstrating numerically how one situation is riskier than the other. a. Derive the probability distribution for total losses under Option A (2 points) 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, recognizing that Rachel now has two machines. (2 points) c. Compare the amount of risk Rachel faces under Option A vs. Option B. Which option has more risk? Justify and demonstrate your answer. (2 points)Explanation / Answer
Solution:
a) Loss = $5,000 with P(loss) = 10% or 0.10
Expected loss = 5,000 * 0.10 = $500
b) Loss = $2500 with P(loss) = 0.10 when machine 1 fails
Loss = $2500 with P(loss) = 0.10 when machine 2 fails
Loss = $5000 with P(loss) = 0.10 * 0.10 = 0.01 When both machine 1 and MAchine 2 fails
So Expected loss = 2500 * 0.10 + 2500 * 0.10 + 5000 * 0.01
= $550
c) Comparing the amount of risk Rachel faces under option A vs. Option B expected loss is more in option B
So, option B has more risk.