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Assuming that the face cards are given numbers (J = 11, Q = 12, K = 13 and A = 1), then the prime numbers that are possible are 2, 3, 5, 7, 11, 13. There are six primes out of 13 possible numbers, giving a probability of 6/13, or about .462 (46.2%).

Note: This ignores the fact that there are four of each number in the deck. It's easy to show that the fours cancel out of the fraction. 24/52 = (6*4)/(13*4) = 3/13.

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