A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that it is :
(i) an ace
(ii) a jack of hearts
(iii) a three of clubs or a six of diamonds
(iv) a heart
(v) any suit except heart
(vi) a ten or a spade
(vii) neither a four nor a club
(viii) a picture card
(ix) a spade or a picture card.

Question

A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that it is :
(i) an ace
(ii) a jack of hearts
(iii) a three of clubs or a six of diamonds
(iv) a heart
(v) any suit except heart
(vi) a ten or a spade
(vii) neither a four nor a club
(viii) a picture card
(ix) a spade or a picture card.

KnowledgeBoat · Accepted Answer

Total cards = 52 ∴ No. of possible outcomes = 52 (i) There are 4 aces in a deck (1 of each suit). ∴ No. of favourable outcomes = 4 P(drawing an ace) = . Hence, probability of drawing an ace = . (ii) There is only one jack of hearts. ∴ No. of favourable outcomes = 1 P(drawing a jack of hearts) = . Hence, probability of drawing a jack of hearts = . (iii) There is one three of clubs and one six of diamonds. ∴ No. of favourable outcomes = 2 P(drawing a three of clubs or a six of diamonds) = . Hence, probability of drawing a three of clubs or a six of diamonds = . (iv) There are 13 hearts in a deck. ∴ No. of favourable outcomes = 13 P(drawing a heart) = . Hence, probability of drawing a heart = . (v) There are 39 other cards except heart. ∴ No. of favourable outcomes = 39 P(drawing any suit except heart) = . Hence, probability of drawing any suit except heart = . (vi) There are 13 spade cards and 3 other 10's (1 of each suit except spade) ∴ No. of favourable outcomes = 16 P(drawing a ten or a spade) = . Hence, probability of drawing a ten or a spade = . (vii) There are 13 club cards and 3 other four cards (1 of each suit apart from club) Total cards = 16 Left cards = 52 - 16 = 36. ∴ No. of favourable outcomes = 36 P(drawing neither a club nor a four) = . Hence, probability of drawing neither a club nor 4 = . (viii) Jack, King and Queen are considered as picture cards. There are 4 jacks, 4 queens and 4 kings ∴ No. of favourable outcomes = 12 P(drawing a picture card) = . Hence, probability of drawing a picture card = . (ix) No. of spade cards = 13 Jack, king and queen except that of spade are 3 each. Total cards = 13 + 3 + 3 + 3 = 22. ∴ No. of favourable outcomes = 22 P(drawing a spade or a picture card) = . Hence, probability of drawing a spade or a picture card = .

Class	Frequencies
0-20	17
20-40	f₁
40-60	32
60-80	f₂
80-100	19

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