Denon is buying a clothes dryer that costs $825.
The clothes dryer has a 1 yr warranty from the manufacturer.
The store sells a 5 yr extended warranty for $110. (This is gain amount.)
The odds against needing repairs over the 5 yr are 3:17
The company estimates that it costs $190 to repair a dryer. (This is loss amount.) Suppose that Denon buys the warranty. What is the expected gain for the store?
Expected gain = (probability of gain) (gain amount) - (probability of loss) (loss amount)
First, we need to calculate the probability of needing repairs over the 5 years based on the odds against needing repairs.
The odds against needing repairs are 3:17, which means that the probability of needing repairs is 3 / (3 + 17) = 3 / 20.
Now we can calculate the expected gain for the store:
Expected gain = (probability of gain) (gain amount) - (probability of loss) (loss amount)
Expected gain = (1 - 3/20) ($110) - (3/20) ($190)
Expected gain = (17/20) ($110) - (3/20) ($190)
Expected gain = $93.50 - $28.50
Expected gain = $65
Therefore, the expected gain for the store if Denon buys the warranty is $65.