Question

A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is –
(1) an ace.
(2) a spade.

Answer 1

(1)
Event A: the card drawn is an ace
∴ n(A) = 4
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{4}{52} \\ =\frac{1}{13} \end{gathered}$$
Hence, the probability that the card drawn is an ace is $\frac{1}{13}$.
(2)
Event B: the card drawn is a spade
∴ n(B) = 13
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{B}\right)=\frac{\mathrm{n}\left(\mathrm{B}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{13}{52} \\ =\frac{1}{4} \end{gathered}$$
Hence, the probability that the card drawn is a spade is $\frac{1}{4}$.