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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.

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Solution

## (1) Event A: the card drawn is an ace ∴ n(A) = 4 $\therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)}\phantom{\rule{0ex}{0ex}}=\frac{4}{52}\phantom{\rule{0ex}{0ex}}=\frac{1}{13}$ 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 $\therefore \mathrm{P}\left(\mathrm{B}\right)=\frac{\mathrm{n}\left(\mathrm{B}\right)}{\mathrm{n}\left(\mathrm{S}\right)}\phantom{\rule{0ex}{0ex}}=\frac{13}{52}\phantom{\rule{0ex}{0ex}}=\frac{1}{4}$ Hence, the probability that the card drawn is a spade is $\frac{1}{4}$.

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