Question

One card is drawn from a pack of$52$cards, each of the$52$cards being equally likely to be drawn. Find the probability that the card is drawn is a face card.

Answer 1

In a pack of cards, there are total$52$cards, among which there are$13-13$cards of - $\text{"Heart", "Spade", "Diamond", "Club"}$.

Among these four types, $\text{Heart and diamond}$ are red-colored cards and $\text{Spade and club}$ are black-colored cards.

Among$13$cards, there are $\text{3 face cards (king, queen and jack), one ace card}$ & $9$ numbered cards are present.

Let's find the probability of getting a face card.

Total number of cards,$\text{n(S)}$ =$52$

Number of face cards, $\text{n(E) = 3×4 = 12}$

$\text{P(getting red card) =}\frac{\text{no of favourable outcomes, n(E)}}{\text{total no of possible outcomes of event, n(S)}}$

$$\begin{gathered} =\frac{12}{52} \\ =\frac{3}{13} \end{gathered}$$

Hence, the probability of getting a face card is$\frac{3}{13}.$