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 (iii) neither a king nor a queen (ii) a red king (iv) either a king or a queen .

Answer 1

A deck of playing cards consists of 52 cards out of which 26 are black cards and  other 26 are red cards, where red cards consists of 13 cards of heart , 13 cards of diamond and black cards consists of 13 cards  of spades and 13 cards are club.
13 cards in each suit are king ,queen, Jack, 10, 9,8,7,6, 5, 4, 3 and 2.

King, queen ,and jack are called face cards. Total number of face cards are 12.

SOLUTION:
Total number of outcomes = 52

i) Favourable outcomes = 13 cards are of spade & 3 are ace (13 Spades + 3 ace )=16
Number of favourable outcomes= 16

Probability = Number of favourable outcomes/ Total number of outcomes.
Required probability = P(spade or ace) = 16/52= 4/13

Hence, the probability that the card  drawn is spade or ace 4/13.

ii) Total number of king and queen cards= 4+4=8
Favourable outcomes = 52 -8= 44
Number of favourable outcomes= 44

Probability = Number of favourable outcomes/ Total number of outcomes.
Required probability = P(neither a king nor a queen) = 44/52= 11/13

Hence, the probability that the card  drawn is neither a king nor a queen 11/13.

iii)Favourable outcomes = 2 red king  cards
Number of favourable outcomes= 2

Probability = Number of favourable outcomes/ Total number of outcomes.

Required probability = P(red king) = 2/52= 1/26
Hence, the probability that the card  drawn is red king 1/26

iv)Total number of king and queen cards= 4+4=8
Number of favourable outcomes= 8

Probability = Number of favourable outcomes/ Total number of outcomes.
Required probability = P(either a king or a queen) = 8/52= 2/13

Hence, the probability that the card  drawn is either a king or a queen 2/13.

HOPE THIS WILL HELP YOU..

Answer 2

ii) 2/52 = 1/26
iv) 8/52
iii)52-8/52