Question

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of getting

(i) a red king,
(ii) a queen or a jack.

Answer 1

Total number of cards = 52

(i) Number of red kings = 2

∴ P(getting a red king) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{2}{52}=\frac{1}{26}$

Thus, the probability of getting a red king is $\frac{1}{26}$.

(ii) Number of queens or jacks = 4 + 4 = 8

∴ P(getting a queen or a jack) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{8}{52}=\frac{2}{13}$

Thus, the probability of getting a queen or a jack is $\frac{2}{13}$.