Question

In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red.

If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?

One-eighth
One-half
Two-thirds
Three-fourths

Answer 1

One-eighth.

With replacement the picks are independent. P(black first) = 26/52 = 1/2, P(heart second) = 13/52 = 1/4, so P = (1/2)(1/4) = 1/8.