Question

Determine the following probabilities. Enter your final answers as reduced fractions.

Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card.

Find the probability that the first card is black and the second card is a Ace.

Answer 1

There are 26 black cards and 4 Aces in a standard deck of 52 cards. The probability of drawing a black card on the first draw is 26/52 = 1/2. Since the first card is replaced, the probability of drawing an Ace on the second draw is still 4/52 = 1/13, regardless of the color of the first card.

Therefore, the probability of drawing a black card first and an Ace second is:

(1/2) x (1/13) = 1/26

So the probability is 1/26.