Question

From a pack of $52$ cards, two cards are drawn one by one without replacement. The probability that first drawn card is a king and second is a queen, is

• A. $\frac{2}{13}$
• B. $\frac{8}{663}$
• C. $\frac{4}{663}$
• D. $\frac{103}{663}$

Answer 1

The correct option is C

$\frac{4}{663}$

Explanation for the correct option:

Step: 1 Find the probability of getting a king at first attempt.

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

There are $4$ kings in that pack.

If one card is drawn at random, then the probability of getting a king is

$$\begin{gathered} =\frac{4}{52} \\ =\frac{1}{13} \end{gathered}$$

Step: 2 Find the probability of getting a queen at second attempt without replacement.

Now, there are $51$ cards in that pack.

There are $4$ queens in that pack.

If one card is drawn at random, then the probability of getting a queen without any replacement is

$=\frac{4}{51}$

Step: 3 Find the required probability

$\therefore$the probability of getting first drawn card is a king and second is a queen $=\frac{1}{13}\times \frac{4}{51}$

$=\frac{\mathbf{4}}{\mathbf{663}}$

Hence, Option (C) is the correct answer.