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

(i) a king of red colour

(ii) a face card

(iii) a red face card

(iv) the jack of hearts

(v) a spade

(vi) the queen of diamonds

No. of possible outcomes = 52.

(i) There is one king of hearts and one king of diamonds in a deck.

No. of favourable outcomes (of getting a king of red colour) = 2

P(drawing a king of red colour)

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

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

(ii) There are 12 face cards (3 of each suit) in a deck.

No. of favourable outcomes (for getting a face card) = 12

P(drawing a face card)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{12}{52} = \dfrac{3}{13}$.

Hence, the probability of drawing a face card = $\dfrac{3}{13}$.

(iii) There are 6 red face cards (3 of hearts and 3 of diamonds) in a deck.

No. of favourable outcomes (for getting a red face card) = 6

P(drawing a red face card)

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

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

(iv) There is one jack of hearts.

No. of favourable outcomes (for getting a jack of hearts) = 1

P(drawing a jack of hearts)

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

Hence, the probability of drawing a jack of hearts = $\dfrac{1}{52}$.

(v) There are 13 spade cards in a deck.

No. of favourable outcomes(for getting a spade) = 13

P(drawing a spade)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{13}{52} =\dfrac{1}{4}$.

Hence, the probability of drawing a spade = $\dfrac{1}{4}$.

(vi) There is 1 queen of diamonds in a deck.

No. of favourable outcomes(for getting queen of diamonds) = 1

P(drawing a queen of diamonds)

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

Hence, the probability of drawing a queen of diamonds = $\dfrac{1}{52}$.