Question

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 spade or an ace.
(ii) a black king.
(iii) neither a jack nor a king.
(iv) either a king or a queen.

Answer 1

Total number of possible outcomes = Total number of cards = 52,
(i) a card of spade or an ace = 13 + 3 (Spades + Aces) = 16 (3 aces because out of 4 aces, one will be ace of spade as well)

(ii) a black king = 2

(iii) neither a jack nor a king = 52 – 4 – 4 = 44

(iv) either a king or a queen = 4 + 4 = 8

• P(Spade or ace) = 16/52 = 4/13

• P(Black king) = 2/52 = 1/26

• P(Neither jack nor king) = 44/52 = 11/13

• P(either a king or queen) = 8/52 = 2/13