Question

A card is drawn at random from well shuffled pack of 52 cards. Find the probability that the card drawn is :
(i) a spade
(ii) not of diamond

Answer 1

Total number of cards = 52
∴ n(S) = 52

(i) Let X be the event that the drawn card is a spade.
We know:
Number of spades = 13
∴ n(X) = 13
Thus, we have:

$$\begin{gathered} \mathrm{P}\left(\mathrm{X}\right)=\frac{n\left(\mathrm{X}\right)}{n\left(\mathrm{S}\right)} \\ \Rightarrow \mathrm{P}\left(\mathrm{X}\right)=\frac{13}{52}=\frac{1}{4} \end{gathered}$$

(ii) Let Y be the event that the drawn card is not a diamond.
∴ n(Y) = 52 $-$ 13 = 39 [Because there are 13 cards of diamonds in a pack]
Thus, we have:

$$\begin{gathered} \mathrm{P}\left(\mathrm{Y}\right)=\frac{n\left(\mathrm{Y}\right)}{n\left(\mathrm{S}\right)} \\ \Rightarrow \mathrm{P}\left(\mathrm{Y}\right)=\frac{39}{52}=\frac{3}{4} \end{gathered}$$