#### 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`