For this problem, use the fact that the expected value of an event is a probabil

Question

For this problem, use the fact that the expected value of an event is a probability weighted average, the sum of each probable outcome multiplied by the probability of the event occurring. You are in the market for a used car. At a used car lot, you know that the blue book value for the cars you are looking at is between $14,000 and $17,000. If you believe the dealer knows more about the cars than you, how much are you willing to pay? Assume that you care only about the expected value of the car you buy and that the car values are symmetrically distributed You are willing to pay $(Round your response to the nearest whole number.)

Explanation / Answer

Solution: $14,000

Working:

Willingness to pay the average price up front = ($14,000 + $17,000) / 2 = $15,500

Since the dealer is aware of this fact thus will only sell a car worth between $14,000 and $15,500

As you know this, thus will be willing to pay = ($14,000 + $15,500) / 2 = $14,750

The logic will continue until you are willing to pay the amount of $14,000

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