**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.

**Solution:**

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

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

(ii) Number of red kings = 2

$\therefore P($ getting a red king $)=\frac{2}{52}=\frac{1}{26}$

(iii) Total number of kings = 4

Total number of queens = 4

Let

Then, the favourable outcomes = 4 + 4 = 8

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

$\therefore P($ 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$\therefore P($ getting neither a king nor a queen $)=1-\left(\frac{2}{13}\right)=\frac{11}{13}$