Question

A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability that the card drawn is (a) a king or a jack (b) a red card (c) neither a king nor a queen.

Answer 1

Total number of all possible outcomes= 52
(a) Total number of kings = 4
Total number of jacks = 4
Let E be the event of getting either a king or a jack.
Then, the favourable outcomes = 4 + 4 = 8
∴ P( getting a king or a jack) = P (E) = $\frac{8}{52}=\frac{2}{13}$

(b) Number of red cards = 26
∴ P( getting a red card) = $\frac{26}{52}=\frac{1}{2}$

(c) Let E be the event of getting either a king or a queen. Then, (not E) is the event that the drawn card is neither a king nor a queen.

Total number of kings = 4
Total number of queens = 4
Then, the favourable outcomes for event E = 4 + 4 = 8
∴ P( getting a king or a queen) = P (E) = $\frac{8}{52}=\frac{2}{13}$

Now, ​P (E) + ​P (not E) = 1
∴ ​P(getting neither a king nor a queen ) = P (not E) = $1-\left(\frac{2}{13}\right)=\frac{11}{13}$