Question

All red face cards are removed from a pack of playing cards. The remaining cards are 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 and (iii) a card of clubs. [CBSE 2015]

Answer 1

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

All the red face cards are removed from the pack. Then,

Number of remaining cards = 52 − 6 = 46

∴ Total number of outcomes = 46

(i) Number of red cards in the remaining pack of cards = 26 − 6 = 20

So, the favourable number of outcomes are 20.

∴ P(drawing a red card) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{20}{46}=\frac{10}{23}$

(ii) There are 6 face cards (2 black jacks, 2 black queens and 2 black kings) in the remaining pack of cards.

So, the favourable number of outcomes are 6.

∴ P(drawing a face card) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{6}{46}=\frac{3}{23}$

(iii) There are 13 cards of club in the remaining pack of cards.

So, the favourable number of outcomes are 13.

∴ P(drawing a card of club) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{13}{46}$