Suppose you are going to draw two cards from a standard deck without replacement. What is the probability that the first card is an odd number card and the second card is a King?

Question

Suppose you are going to draw two cards from a standard deck without replacement. What is the probability that the first card is an odd number card and the second card is a King?

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Answer 1

Since the cards are: A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, there are actually only 4 that are odd numbers (3, 5, 7, and 9). But there are 4 suits. So 4•4 = 16. Since there are 52 total cards, the probability that the first card is an odd number card is 16/52 or (dividing top and bottom by 4) 4/13

For the second draw, we don't replace the "odd card" but the King is not an odd card, so there are still 4 kings in the deck. However, there are only 51 cards. So the probability of the second draw being a King is 4/51.

The probability of both happening is 4/13•4/51 = 16/2652 = 4/663 or 0.6033%