Question

One card is drawn at random from pack of $52$ cards. What is the probability that the card drawn is a face card?

• A. $\frac{1}{13}$
• B. $\frac{4}{13}$
• C. $\frac{1}{4}$
• D. $\frac{9}{52}$

Answer 1

The correct option is B

$\frac{4}{13}$

Finding the probability of the card drawn is a face card:

Let $E$ be the event of card drawn is a face card.

Sample space of the event $\left(S\right)=52$

Number of face card in the deck of cards $=4\left(4facecardsofeachtype\right)=16$

So, $n\left(E\right)=16;n\left(S\right)=52$

Probability of the card drawn is a face card is $=\frac{n\left(E\right)}{n\left(S\right)}$

$$\begin{gathered} \therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)} \\ \Rightarrow P\left(E\right)=\frac{16}{52} \\ \Rightarrow P\left(E\right)=\frac{4}{13} \end{gathered}$$

Hence, option (b) is correct.