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

There are $26$ black cards in a deck of $52$ cards.

Let $P\left(A\right)$ be the probability of getting a black card in the first draw.

$\therefore P\left(A\right)=\frac{26}{52}=\frac{1}{2}$

Let $P\left(B\right)$ be the probability of getting a black card on the second draw.

Since the card is not replaced,

$\therefore P\left(B\right)=\frac{25}{51}$
Thus, probability of getting both the cards black $=\frac{1}{2}\times \frac{25}{51}=\frac{25}{102}=0.24$.