Question

Two cards are drawn from a pack of $52$ cards.

What is the probability that one of them is a queen and the other is an ace

• A. $\frac{2}{663}$
• B. $\frac{2}{13}$
• C. $\frac{4}{663}$
• D. None of these

Answer 1

The correct option is D

None of these

Find the required probability:

In the question, it is given that two cards are drawn at random from the pack of $52$ cards.

We know that there are $4$ queens and $4$ aces in the pack of $52$ cards.

So, the total number of ways of selecting one queen out of four is $4$.

And the total number of ways of selecting one ace out of four is $4$.

Therefore, the number of outcomes in favour is $4·4=16$.

Also, the number of ways of selecting two cards out of the pack of $52$ cards is ${}^{52}C_2=1326$.

So, the required probability can be given by $\frac{16}{1326}=\frac{8}{663}$.

Therefore, the required probability is $\frac{8}{663}$.

Hence, option (D) is the correct answer.