Question

Two cards are drawn from a regular deck of 52 cards without replacement. What is the probability that the first card is an ace of clubs and the second is black?

Answer 1

Two cards are drawn from a regular deck of 52 cards without replacement. What is the probability that the first card is an ace of clubs and the second is black?

There are total 52 cards, 26 of them are black. The ace of clubs is also a black card.

The probability that first card is an ace of clubs = 1/52

After first selection, total number of cards = 52-1 = 51 and total black cards = 26-1 = 25

The probability that the second is black given first card is an ace of clubs = 25/51

Therefore, the probability that the first card is an ace of clubs and the second is black is:

The probability that first card is an ace of clubs * The probability that the second is black given first card is an ace of clubs

            = (1/52) * (25/51) = 0.0094