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

Answer 1

1st card is Ace, 2nd is black (spade or club), out of 52 standard deck of cards

4 Aces out of 52 = 4/52 = 1/13 chance of an Ace on one random draw

without replacement 2nd card is black, which was originally 1/2 the deck 26 out of 52 cards

but since one card was removed and not replaced, what's left is still the same odds, since we don't know what color the ace was. Without replacement or with replacement would have made no difference in this problem.

(1/13) x (1/2) = 1/26 = probability of Ace, then Black card

P(A then B) = 1/26 = about 0.0385 = about 3.85%