Question

Two cards are drawn one by one at random from a pack of $52$ cards. The probability that both of them are king, is

• A. $\frac{2}{13}$
• B. $\frac{1}{169}$
• C. $\frac{1}{221}$
• D. $\frac{30}{221}$

Answer 1

The correct option is C

$\frac{1}{221}$

Find the required probability:

There are $52$ cards in a full pack of cards.

There are $4$ kings in a pack.

The probability that the first card drawn is a king $=\frac{4}{52}$

Now there are $51$ cards remaining in the pack out of which $3$ are kings.

The probability of of the second card drawn being a king $=\frac{3}{51}$

Hence, the probability that both the cards drawn are kings $=\frac{4}{52}\times \frac{3}{51}$

$=\frac{1}{13}\times \frac{1}{17}$

$=\frac{1}{221}$

Therefore, the probability that both cards drawn being kings from a pack of $52$ cards is $\frac{1}{221}$.

Hence, option (C) is the correct answer.