Question

All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting

(i) face card
(ii) red card
(iii) black card
(iv) king

Answer 1

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

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

Number of remaining cards = 52 − 6 = 46

∴ Total number of outcomes = 46

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

So, the favourable number of outcomes are 6.

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

(ii) There are 26 red cards in the remaining pack of cards.

So, the favourable number of outcomes are 26.

∴ P(getting a red card) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{26}{46}=\frac{13}{23}$

(iii) Number of black cards in the remaining pack of cards = 26 − 6 = 20

So, the favourable number of outcomes are 20.

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

(iv) There are 2 red king cards in the remaining pack of cards.

So, the favourable number of outcomes are 2.

∴ P(getting a king) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{2}{46}=\frac{1}{23}$