Alice proposes to Bob the following game. Bob pays one dollar to play. Fifty balls marked 1,2,....,50 are placed in a big jar, stirred around, and then drawn out one by one by Zori, who is wearing a blindfold. The result is a random permutation ? of the integers 1, 2,...,50. Bob wins with a payout of two dollars and fifty cents if the permutation ? is a derangement, i.e., ? (i) ≠ i for all i = 1, 2,..., n. Is this a fair game for Bob? If not how should the payoff be adjusted to make it fair?