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A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that the card drawn is (i) a card of spades or an ace, (ii) a black king, (iii) neither a jack nor a king, (iv) either a king or a queen. Select the correct answer from above options

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Total number of all possible outcomes = 52. (i) There are 13 cards of spades including one ace and there are 3 more aces. So, the number of favourable cases = 13+3= 16. ∴ P(getting a card of spades or an ace ) = 16 52 = 4 13 . (ii) There are 2 black kings. ∴ P(getting a black king) = 2 52 = 1 26 . (iii) There are 4 jacks and 4 kings. So, the number of cards which are neither jacks nor kings ={52-(4+4)}=44. ∴ P(getting a card which is neither a jack nor a king) = 44 52 = 11 13 . (iv) There are 4 kings and 4 queens. So, the number of cards which are either kings or queens = 4+4= 8. ∴ P(getting a card which is either a king or a queen) = 8 52 = 2 13 .

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