Question

All face cards of spades are removed from a pack of 52 playing cards and the remaining pack is shuffled well. A card is then drawn at random from the remaining pack. Find the probability of getting:

1. a face card 
2. an ace or a jack

Answer 1

Given: Total cards = 52

Face cards of spades removed = King, Queen, Jack of spades = 3 cards 

\[ \text{Remaining total cards, } n(S) = 52 - 3 = 49 \]

(i) A face card: Total original face cards = 12

Remaining face cards = `(12 - 3 = 9)`

\[ P(\text{face card}) = \dfrac{9}{49} \]

(ii) An ace or a jack: Number of aces = 4 (none removed)

Number of jacks = `(4 - 1\ \text{(Jack of spades)} = 3)`

Total favourable cards = (4 + 3 = 7) 

\[ P(\text{ace or a jack}) = \dfrac{7}{49} = \dfrac{1}{7} \]