#### Question

All red face cards are removed from a pack of playing cards. The remaining cards were well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is

(i) a red card

(ii) a face card

(iii) a card of clubs

#### Solution

Total number of cards in a deck = 52

Number of red face cards in a deck = 6

Number of cards left in the deck if all red face cards are removed = 52−6 = 46

(i)Total number of red cards left in the deck = 26−6 = 20

Probability that the card drawn is red = `"Total favourable number of cards"/"Total number of cards"=20/46=10/23`

(ii)Total number of face cards left in the deck = 12−6 = 6

Probability that the card drawn is a face card = `"Total favourable number of cards"/"Total number of cards"=6/46=3/23`

(iii)Total number of cards of clubs in the deck = 13

Probability that the card drawn is a card of clubs = `"Total favourable number of cards"/"Total number of cards"=13/46`