A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting :
(i) '2' of spades
(ii) a jack
(iii) a king of red colour
(iv) a card of diamond
(v) a king or a queen
(vi) a non-face card
(vii) a black face card
(viii) a black card
(ix) a non-ace
(x) non-face card of black colour
(xi) neither a spade nor a jack
(xii) neither a heart nor a red king.

Question

A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting :
(i) '2' of spades
(ii) a jack
(iii) a king of red colour
(iv) a card of diamond
(v) a king or a queen
(vi) a non-face card
(vii) a black face card
(viii) a black card
(ix) a non-ace
(x) non-face card of black colour
(xi) neither a spade nor a jack
(xii) neither a heart nor a red king.

KnowledgeBoat · Accepted Answer

Well-shuffling ensures equally likely outcomes. Total number of outcomes = 52. (i) There is only one 2 of spades in the whole pack. ∴ P('2' of spades) = . Hence, the probability of drawing 2 of spades = . (ii) There are 4 jacks, one of each suit. ∴ The number of favourable outcomes to the event 'a jack' = 4. ∴ P(a jack) = . Hence, the probability of drawing a jack = . (iii) There are two king of red colour, one of hearts and one of diamond. ∴ The number of favourable outcomes to the event 'king of red colour' = 2. ∴ P(king of red colour) = Hence, the probability of drawing a king of red colour = . (iv) There are 13 cards of diamond suit. ∴ The number of favourable outcomes to the event 'a card of diamond' = 13. ∴ P(a card of diamond) = . Hence, the probability of drawing a diamond card = . (v) There are 8 king and queen cards, 2 in each suit. ∴ The number of favourable outcomes to the event 'a king or queen' = 8. ∴ P(a king or queen) = . Hence, the probability of drawing a king or queen = . (vi) There are 12 face cards. ∴ No. of non-face cards = 52 - 12 = 40. ∴ The number of favourable outcomes to the event 'a non-face card' = 40. ∴ P(a non-face card) = . Hence, the probability of drawing a non-face card = . (vii) Since 2 suits are of black colour and each suit has 3 face cards. ∴ No. of black face cards = 2 × 3 = 6. ∴ The number of favourable outcomes to the event 'a black face card' = 6. ∴ P(a black face card) = . Hence, the probability of drawing a black face card = . (viii) There are 2 suits of black cards. ∴ No. of black cards = 26. ∴ The number of favourable outcomes to the event 'a black card' = 26. ∴ P(a black card) = . Hence, the probability of drawing a black card = . (ix) There are 4 ace cards, one in each suit. ∴ No. of non-ace cards = 52 - 4 = 48. ∴ The number of favourable outcomes to the event 'a non-ace card' = 48. ∴ P(a non-ace card) = . Hence, the probability of drawing a non-ace card = . (x) There are 3 face cards in each suit and 2 suits of black colour. Hence, no. of face cards of black colour = 6. ∴ No. of non-ace black cards = 26 - 6 = 20. ∴ The number of favourable outcomes to the event 'a non-face card of black colour' = 20. ∴ P(a non-face black card) = . Hence, the probability of drawing a non-face black card = . (xi) There are 13 spade cards and each suit has 1 jack. So, the other 3 suits apart from spade has 3 jacks. ∴ Total no. of spade and jack cards = 13 + 3 = 16. Hence, no. of cards other than spade and jack = 52 - 16 = 36. ∴ The number of favourable outcomes to the event 'neither a spade nor a jack' = 36. ∴ P(neither a spade nor a jack) = . Hence, the probability of drawing neither a spade nor a jack = . (xii) There are 13 heart cards and 2 suits of red colour. Since, one king of red colour is already included in hearts hence only one red king is more. ∴ Total no. of heart and red king cards = 13 + 1 = 14. Hence, no. of cards other than heart and red king cards = 52 - 14 = 38. ∴ The number of favourable outcomes to the event 'neither heart nor a red king' = 38. ∴ P(neither a heart nor a red king) = . Hence, the probability of drawing neither a heart nor a red king = .

Mathematics

Probability

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