# All the black face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a - Mathematics

All the black face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a:
(i) face card
(ii) red card
(iii) black card
(iv) king

#### Solution

Since all the black face cards were removed from the pack, so there are 26 red cards and 20 black cards left in the pack.

∴ Total numbers of remaining cards in the pack = 26 + 20 = 46

(i)
Total number of possible outcomes = 46

In the remaining 46 cards, there are 6 red face cards i.e. a king card, a queen card and a jack card each of diamond and heart suits.

Total number of favourable outcomes =  6

∴ Probability of getting a face card ="Total number of favourable outcomes"/"Total number of outcomes"=6/46=3/23

ii)
Total number of possible outcomes = 46

There are 26 red cards remaining in the pack.

Total number of favourable outcomes = 26

∴ Probability of getting a red card ="Total number of favourable outcomes"/"Total number of outcomes"=26/46=13/23

(iii)
Total number of possible outcomes = 46

There are 20 black cards remaining in the pack.

Total number of favourable outcomes = 20

∴ Probability of getting a black card  ="Total number of favourable outcomes"/"Total number of outcomes"=20/46=10/23

(iv)
Total number of possible outcomes = 46

There are 2 king cards of red colour in the remaining 46 cards.

Total number of favourable outcomes = 2

∴ Probability of getting a king card ="Total number of favourable outcomes"/"Total number of outcomes"=2/46=1/23

Concept: Basic Ideas of Probability
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2013-2014 (March) Delhi Set 2

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