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Problem 7. (20 pts) The following Problem comes from the game of Treize, featuring prominently in one of the earliest probability books, by P.R. de Montmort2. The game can be described as follows. Consider the 13 cards of a given suit, so there are 13 different values, and draw them face down to the table. Each player calls out a number between 1 and 13 and turns one card face up. A player loses if the called value coincides with the card value. If no player loses by the time the last card is turned face up, then the dealer loses. (a) Compute the probability that the dealer loses. b) Suppose that we played with 1982 distinct cards with values from 1 to 1982. Estimate the probability that the dealer loses.

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