Question

A card is drawn at random form a well-shuffled deck of playing cards. Find the probability that the card drawn is
(i) a card of spades of an ace
(ii) a red king
(iii) either a king or a queen
(iv) neither a king nor a queen.

Answer 1

Total number of all possible outcomes= 52
(i) Number of spade cards = 13
Number of aces = 4 (including 1 of spade)

Therefore, number of spade cards and aces = (13 + 4 − 1) = 16

∴ P( getting a spade or an ace card) = $\frac{16}{52}=\frac{4}{13}$

(ii) Number of red kings = 2
∴ P( getting a red king) = $\frac{2}{52}=\frac{1}{26}$

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

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

queen.

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