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

(i) Cards of spade or an ace = 13 + 3 = 16 

Total no. of cards = 52 

P (spade or an ace) = 16/52 = 4/13 

(ii) Black kings = 2

P (a black king) = 2/52 =1/26

(iii) Jack or king = 4 + 4 = 8 

P (neither jack nor a king) = 1 - 8/52  = (52 - 8)/ 52 = 44/52 = 11/13

(iv) King or queen = 4 + 4 = 8 

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