Question

All the face cards are removed from the pack of 52 cards and a card is drawn at random from the remaining cards. Find the probability that the card so drawn is

1. a spade. 
2. not an ace.

Answer 1

Given: Total cards = 52

Face cards removed = 12 (3 from each suit) 

\[ \text{Remaining total cards, } n(S) = 52 - 12 = 40 \]

(i) A spade: Original number of spade cards = 13

Spade face cards removed = 3

Remaining spade cards = `(13 - 3 = 10)` 

\[ P(\text{spade}) = \dfrac{10}{40} = \dfrac{1}{4} \]

(ii) Not an ace: None of the aces are face cards, so all 4 aces remain.

Remaining cards that are not aces = `(40 - 4 = 36)` 

\[ P(\text{not an ace}) = \dfrac{36}{40} = \dfrac{9}{10} \]