Question

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability of drawing a (i) face card (ii) card which is neither a king nor a red card.

Answer 1

Total number of all possible outcomes= 52
(i) We know that kings, queens and jacks are the face cards.

Number of face cards = 12

Let E₁ be the event of getting a face card.
Then, the number of favourable outcomes = 12
∴ P( getting a face card) = P (E₁) = $\frac{12}{52}=\frac{3}{13}$

(ii) There are 26 red cards (including 2 kings) and there are 2 more kings.
Therefore, number of cards, each one of which is either a red card or a king = 26 + 2 = 28
Let E₂ be the event that the card drawn is neither a king nor a red card.
Then, the number of favourable outcomes = (52 − 28) = 24
∴ P( getting neither a king nor a red card) = P (E₂) = $\frac{24}{52}=\frac{6}{13}$