From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn will :

(i) be a black card.

(ii) not be a red card.

(iii) be a red card.

(iv) be a face card.

(v) be a face card of red colour.

We know that,

Total number of cards = 52

So, the total number of outcomes = 52

There are 13 cards of each type. The cards of heart and diamond are red in colour. Spade and clubs are black. Hence, there are 26 red cards and 26 black cards.

(i) Number of black cards in a deck = 26 (13 spade + 13 club)

∴ Number of favourable outcomes = 26

P(of drawing a black card) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{26}{52} = \dfrac{1}{2}$.

Hence, probability of drawing a black card = $\dfrac{1}{2}$.

(ii) Number of red cards in a deck = 26

∴ Number of non-red (black) cards = 52 - 26 = 26.

∴ Number of favourable outcomes = 26

P(of not drawing a red card) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{26}{52} = \dfrac{1}{2}$.

Hence, probability of not drawing a red card = $\dfrac{1}{2}$.

(iii) Number of red cards in a deck = 26.

∴ Number of favourable outcomes = 26

P(of drawing a red card) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{26}{52} = \dfrac{1}{2}$.

Hence, probability of drawing a red card = $\dfrac{1}{2}$.

(iv) There are 12 face cards (4 kings, 4 queens and 4 jacks) in a deck.

∴ Number of favourable outcomes = 12

P(of drawing a face card) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{12}{52} = \dfrac{3}{13}$.

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

(v) There are 26 red cards in a deck, and 6 of these cards are face cards (2 kings, 2 queens and 2 jacks).

∴ Number of favourable outcomes = 6

P(of drawing a red face card) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{6}{52} = \dfrac{3}{26}$.

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