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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

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Solution

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: $\mathrm{P}\left(\mathrm{X}\right)=\frac{n\left(\mathrm{X}\right)}{n\left(\mathrm{S}\right)}\phantom{\rule{0ex}{0ex}}⇒\mathrm{P}\left(\mathrm{X}\right)=\frac{13}{52}=\frac{1}{4}$ (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: $\mathrm{P}\left(\mathrm{Y}\right)=\frac{n\left(\mathrm{Y}\right)}{n\left(\mathrm{S}\right)}\phantom{\rule{0ex}{0ex}}⇒\mathrm{P}\left(\mathrm{Y}\right)=\frac{39}{52}=\frac{3}{4}$

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