Question

a player is dealt one card from a 52 card deck. then the card is replaced in the deck, the deck is shuffled, and the player draws again. find the probability of the player getting the picture card the first timeand a diamond the second time. express the probability as a simplified fraction

Answer 1

The answer is 3/52.

There are 12 face cards in a standard deck, so the probability of the first card is 12/52 = 3/13.

After replacement, there are 13 diamonds in the deck that still contains 52 cards; 13/52 = 1/4.

Together the probability is 3/13(1/4) = 3/52.