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,
(iii) a card of clubs.

Answer 1

There are 6 red face cards. These are removed.

Thus, remaining number of cards = 52 − 6 = 46.

(i) Number of red cards now = 26 − 6 = 20.

∴ P(getting a red card) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{20}{46}=\frac{10}{23}$

Thus, the probability that the drawn card is a red card is $\frac{10}{23}$.

(ii) Number of face cards now = 12 − 6 = 6.

∴ P(getting a face card) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{6}{46}=\frac{3}{23}$

Thus, the probability that the drawn card is a face card is $\frac{3}{23}$.

(iii) Number of card of clubs = 12.

∴ P(getting a card of clubs) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{12}{46}=\frac{6}{23}$

Thus, the probability that the drawn card is a card of clubs is $\frac{6}{23}$.