Q. 2 4.3( 36 Votes )

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.

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 = .


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