Problem 5 A box contains 8 coins, 2 of which are counterfeit. Coins are removed from the box, one at a time, until both countefeit coins are found. Let X be the number of coins removed to find the first counterfeit one, and let Y be the number of additional coins removed to find the second counterfeit one. (a) Find the joint pmf of X and Y. (b) Find the probability that not all of the coins will be removed from the box.

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