Question

Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is

(i) a king (ii) of red colour (iii) a face card (iv) a queen [CBSE 2014]

Answer 1

In a pack of 52 playing cards, there are 2 red queens and 2 black jacks.

Red queens and black jacks are removed from the pack. Then,

Number of remaining cards = 52 − 4 = 48

∴ Total number of outcomes = 48

(i) There are 4 king cards in the remaining pack of cards.

So, the favourable number of outcomes are 4.

∴ P(drawing a king) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{4}{48}=\frac{1}{12}$

(ii) Two red queens are removed from the pack of cards.

Number of red cards in the remaining pack of cards = 26 − 2 = 24

So, the favourable number of outcomes are 24.

∴ P(drawing a red card) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{24}{48}=\frac{1}{2}$

(iii) There are 12 face cards in the pack, out of which 2 red queens and 2 black jacks are removed.

Number of face cards in the remaining pack of cards = 12 − (2 + 2) = 8

So, the favourable number of outcomes are 8.

∴ P(drawing a face card) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{8}{48}=\frac{1}{6}$

(iv) There are 4 queen cards in the pack, out of which 2 red queens are removed.

Number of queens in the remaining pack of cards = 4 − 2 = 2

So, the favourable number of outcomes are 2.

∴ P(getting a queen) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{2}{48}=\frac{1}{24}$