Question

Suppose two cards are drawn in succession (without replacement) from a standard deck of cards.

What is the probability that a face card is drawn first? (Enter your probability as a fraction.)

What is the probability that a face card is drawn second, given that a face card was drawn first? (Enter your probability as a fraction.)

What is the probability of drawing two cards in succession (without replacement) from a standard deck and having them both be face cards? Round to the nearest thousandth.

Answer 1

There are 12 face cards in a deck of 52 cards.

The probability that a face card is drawn first = 12/52 = 0.2308

If a face card is drawn first, then in the second case there are 11 face cards out of 51 remaining cards. Hence, the probability that a face card is drawn second, given that a face card was drawn first = 11/51 = 0.2157

The probability of drawing two cards in succession (without replacement) from a standard deck and having them both be face cards = (12/52) * (11/51) = 0.0498