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.
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.

Given: A pack of 52 cards.

As we all know, there are a total of 26 black cards. Let A and B represent the first and second drawn cards being black, respectively.

Now if the probability of event A, P(A)=P( black card in first draw )=26 / 52=1 / 2

Because the second card is drawn without being replaced, the total number of black cards will now be 25 and the total number of cards will be 51, which is the conditional probability of B if A has already occurred.

Now, P(B / A)=P( black card in second draw) =25 / 51

Thus the probability that both the cards are black

\Rightarrow P(A \cap B)=1 / 2 \times 25 / 51=25 / 102

Answer: The probability that both the cards are black = 25 / 102.