# 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 - Mathematics

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 = 526 = 46

(i)Total number of red cards left in the deck = 266 = 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 = 126 = 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

Concept: Basic Ideas of Probability
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