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

Number of exhaustive cases = 52

Number of black cards = 26

One black card may be drawn in 26 ways.

Therefore, probability of drawing a black card = $P\left(A\right)=\frac{26}{52}=\frac{1}{2}$

After drawing one card, number of cards left = 51

After drawing a black card, number of black cards left = 25

Therefore,

Probability of getting both the black cards = $P\left(A\right).P\left(B|A\right)=\frac{1}{2}\times \frac{25}{51}=\frac{25}{102}$