Question

From a pack of 52 playing cards two cards are drawn at random without replacement. What is the probability of choosing both Face cards?

• A. $\frac{11}{221}$
  
• B. $\frac{1}{221}$
• C. $\frac{33}{221}$
• D. $\frac{9}{221}$

Answer 1

The correct option is A $\frac{11}{221}$


Given, two cards are drawn one after the other from a pack having $52$ cards without replacement.

Number of face cards $=12$

Let $\text{A}$ and $\text{B}$ be two events of drawing first and second Face card without replacement respectively.

Probability of choosing first Face card is $\text{P(A)}=\frac{12}{52}=\frac{3}{13}$

Probability of choosing second Face card is $\text{P(B)}=\frac{11}{51}$

We have to calculate the probability of getting both Face card which is equal to $\text{P(F)}.$

$\Rightarrow \text{P(F)}=\text{P(A)}\times \text{P(B)}$

$\Rightarrow \text{P(F)}=\frac{3}{13}\times \frac{11}{51}=\frac{11}{221}$