Question

From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is

(i) Red and a king

(ii) Either red or a king

Answer 1

Let S denote the sample space. Then, $n\left(S\right)=52$

(i) Let $E_1=$ event of drawing a red card which is a king.

We know that the number of red kings is 2. So, $n\left(E_1\right)=2$

$\therefore$ P(getting a red king) $=P\left(E_1\right)=\frac{n\left(E_1\right)}{n\left(S\right)}=\frac{2}{52}=\frac{1}{26}$

(ii) Let $E_2=$ event of drawing a card which is either red or a king. There are 26 red cards (including 2 red kings) and there are 2 more kings.

$\therefore n\left(E_2\right)=(26+2)=28$

$\therefore$ P(getting a red card or a king) $=P\left(E_2\right)=\frac{n\left(E_2\right)}{n\left(S\right)}=\frac{28}{52}=\frac{7}{13}$.