A card is drawn at random from a well-shuffled deck of playing cards.
Find the probability that the card drawn is
(i) a card of spades or an ace (ii) a red king
(iii) either a king or a queen (iv) neither a king nor a queen.

Answer

` (i) 4/13 (ii) 1/26 (iii) 2/13 (iv) 11/13 `

Explanation

(i) There are 13 cards of spades including 1 ace and 3 more aces are there.
` :. ` P(getting a card of spades or an ace) ` = (13+3)/52 = 16/52 = 4/13`.
(ii) There are 2 red kings.
` :. ` P(getting a red king) ` = 2/52 = 1/26`.
(iii) There are 4 kings and 4 queens.
` :. ` P(getting either a kings or a queen) ` (4+4)/ 52 = 8/52 = 2/13`.
(iv) P(neither a kings nor a queen) = 1-P(either a kings or a queen)
` = (1-2/13) = 11/13`.