Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

Question

Philoid · Accepted Answer

Given: A pack of 52 cards.

As we know there are 26 cards in total which are black. Let A and B denotes respectively the events that the first and second drawn cards are black.

Now, P(A) = P(black card in first draw) =

Because the second card is drawn without replacement so, now the total number of black card will be 25 and total cards will be 51. i.e. the conditional probability of B given that A has already occurred.

Now, P = P(black card in second draw) =

Thus the probability that both the cards are black:

⇒ P(A ∩ B) =

Hence, the probability that both the cards are black = .