Question

All jacks, queens and kings are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a black face card (ii) a red card. [CBSE 2014]

Answer 1

In a pack of 52 playing cards, there are 4 jack, 4 queen and 4 king cards.

All jack, queen and king cards are removed from the pack. Then,

Number of remaining cards = 52 − 12 = 40

∴ Total number of outcomes = 40

(i) There are 0 face cards in the remaining pack of cards.

So, the favourable number of outcomes are 0.

∴ P(drawing a black face card) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{0}{40}=0$

(ii) There are 2 red jacks, 2 red queens and 2 red kings among 4 jack, 4 queen and 4 king cards removed from the pack.

Number of red cards in the remaining pack of cards = 26 − (2 + 2 + 2) = 20

So, the favourable number of outcomes are 20.

∴ P(drawing a red card) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{20}{40}=\frac{1}{2}$