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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.

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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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