You are in the market for a used car and see an ad for the model that you like. The owner has not set a price but invites potential buyers to make offers.

Your prepurchase inspection gives you only a very rough idea of the value of the car; you think it is equally likely to be anywhere in the range of $1,000 to $5,000 (so your calculation of the average of this value is $3,000).

The current owner knows the exact value and will accept your offer if it exceeds that value. If your offer is accepted and you get the car, then you will find out the truth.

But you have some special repair skills and know that, when you own the car, you will be able to work on it and increase its value by a third (33.3 . . . %) of whatever it is worth.

(a) What is your expected profit if you offer $3,000? Should you make such an offer?

(b) What is the highest offer that you can make without losing money on the deal?