One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting :

(i) a queen of red color

(ii) a black face card

(iii) the jack or the queen of the hearts

(iv) a diamond

(v) a diamond or a spade

We have,

Total possible outcomes = 52

(i) Number of queens of red color = 2 (1 of each heart and diamond)

∴ Number of favorable outcomes = 2

P(drawing a queen of red colour)

= $\dfrac{\text{No. of favourable outcomes}}{\text{\text{No. of possible outcomes}}} = \dfrac{2}{52} = \dfrac{1}{26}$.

Hence, the probability of drawing a queen of red colour = $\dfrac{1}{26}$.

(ii) Number of black face cards = 6 (3 of each club and spades)

∴ Number of favorable outcomes = 6

P(drawing a black face card)

= $\dfrac{\text{No. of favourable outcomes}}{\text{\text{No. of possible outcomes}}} = \dfrac{6}{52} = \dfrac{3}{26}$.

Hence, the probability of drawing a black face card = $\dfrac{3}{26}$.

(iii) Favorable outcomes for jack or the queen of hearts = 2 (1 jack + 1 queen)

∴ Number of favorable outcomes = 2

P(drawing a jack or the queen of hearts)

= $\dfrac{\text{No. of favourable outcomes}}{\text{\text{No. of possible outcomes}}} = \dfrac{2}{52} = \dfrac{1}{26}$.

Hence, the probability of drawing a jack or the queen of hearts = $\dfrac{1}{26}$.

(iv) Number of diamond cards = 13

∴ Number of favorable outcomes = 13

P(getting a diamond) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{13}{52} = \dfrac{1}{4}$.

Hence, the probability of getting a diamond = $\dfrac{1}{4}$.

(v) Number of favorable outcomes for a diamond or a spade = 13 + 13 = 26.

P(getting a diamond or spade)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{26}{52} = \dfrac{1}{2}$.

Hence, the probability of getting a diamond or spade = $\dfrac{1}{2}$.