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Question

# A card is drawn at random from a well shuffled pack of 52 cards.Find the probability that the card drawn is : (ii) a spade or a face card.

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Solution

## Total number of cards = 52 ∴ n (S) = 52 Let C be the event of drawing a spade card and D be the event of drawing a face card. We know: Number of spade cards = 13 $\therefore$ n (C) = 13 Number of face cards = 12 $\therefore$ n (D) = 12 And number of face cards of spade = 3 $\therefore$ n (C $\cap$ D) = 3 P (C) = $\frac{n\left(C\right)}{n\left(S\right)}=\frac{13}{52}=\frac{1}{4}$ P (D) = $\frac{n\left(D\right)}{n\left(S\right)}=\frac{12}{52}=\frac{3}{13}$ And, P (C $\cap$ D) = $\frac{n\left(C\cap D\right)}{n\left(S\right)}=\frac{3}{52}$ Now, on applying the addition theorem of probability, we get: P (C $\cup$ D) = P (C) + P (D) $-$ P (C $\cap$ D) = $\frac{1}{4}+\frac{3}{13}-\frac{3}{52}=\frac{11}{26}$ $\therefore$ Probability of drawing a spade card or a face card = $\frac{11}{26}$

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