Debbie’s Pizza Palace has one oven to cook pizza. It is a very large oven; it ha

Question

Debbie’s Pizza Palace has one oven to cook pizza. It is a very large oven; it has 5% chance in any one year of being destroyed. If it is destroyed, the machine will cost $7,500 to replace. (Option A) Debbie is considering selling the large oven and buying two smaller ovens. A small oven would cost $3,750 to replace if it is destroyed, and it has a 5% chance of being destroyed.

a. Derive the probability distribution for total losses under Option A

b. Derive the probability distribution for total losses under Option B.

c. Compare the amount of risk Debbie faces under Option A vs. Option B. Which option has more risk? Justify and demonstrate your answer.

Explanation / Answer

a) Loss=7500 :P(x)=0.05

Loss=0 P(x)=0.95

b) Loss=7500 P(x)=0.05^2=0.0025

Loss=3750 P(x)=2*0.05*0.95=0.095

Loss= 0 P(x) = 0.95^2=0.9025

c) Option A has more risk because theere is higher probability for loss of 7500 vs in option B.

If we calculate the standard deviation , we will find that the standard deviation is lower in B than A.

Option B has losses more spread out such that there is an option of middle losses as well

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