Two cards are drawn at random from a standard deck of cards. What is the probability that both will be queens?

Question

Two cards are drawn at random from a standard deck of cards. What is the probability that both will be queens?

Answer 1

1 in 13 chance its a queen

Answer 2

A standard deck has 52 cards, and 4 of those cards are queens.

Therefore, there is a 4/52, or 1/13, chance that the first card drawn will be a queen.

Since we are trying to find the probability of BOTH drawn cards being queens, we must now assume that the first card drawn was a queen.  Therefore, there would now be 51 cards left in the deck, and 3 queens left.  So for the second draw, there is a 3/51 chance of drawing a queen.

To find the probability of BOTH cards being queens, we multiply the two probabilities together.  So:

1/13 x 3/51 = 3/663

                     = 1/221

Therefore, there is a 1/221 chance of both drawn cards being queens.

Answer 3

2 from a standard deck of cards