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 drawn is red and a king.

• A. $\frac{1}{13}$
• B. $\frac{1}{52}$
• C. $\frac{1}{26}$
• D. $\frac{5}{6}$

Answer 1

The correct option is C

$\frac{1}{26}$

Explanation for the correct option:

Finding the required probability:

Let $S$ be the set of all possible outcomes. There are total $52$ cards in a pack.

$\Rightarrow n\left(S\right)=52$

Let $A$ be the event that the card drawn is red and a king. There are only two red kings in a pack of cards.

$\Rightarrow n\left(A\right)=2$

Therefore, the required probability $P\left(A\right)$ will be $\frac{n\left(A\right)}{n\left(S\right)}=\frac{2}{52}=\frac{1}{26}$.

Hence, the correct answer is option C.