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Question
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`
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