Question

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 1

S = 52 cards
⇒ 52 Two cards are drawn without replacement.

A = {26 black cards}
⇒ n(A) = 26

P(A) = $\frac {26}{52}$

And P(B) i.e., the probability that the second card is black known that the first card is black = $\frac {25}{51}$

P(A and B) = P(A).P(B)

= $\frac {26}{52} ×\frac {25}{51}$

= $\frac {1}{2} ×\frac {25}{51}$

= $\frac {25}{102}$