Question

From a pack of 52 cards, all aces and all kings are removed. A card is drawn at random from the remaining cards. Find the probability that the card so drawn is

1. a face card. 
2. a card of red colour.

Answer 1

Given: Total cards = 52

Cards removed = 4 Aces + 4 Kings = 8 cards

\[ \text{Remaining total cards, } n(S) = 52 - 8 = 44 \]

(i) A face card: Original face cards = 12 (4 Kings, 4 Queens, 4 Jacks).

Since all 4 Kings are removed, only Queens and Jacks remain.

Number of remaining face cards = `(4 + 4 = 8)` 

\[ P(\text{face card}) = \dfrac{8}{44} = \dfrac{2}{11} \]

(ii) A card of red colour: Original red cards = 26

Red cards removed = 2 red Aces + 2 red Kings = 4 cards

Remaining red cards = `(26 - 4 = 22)` 

\[ P(\text{red card}) = \dfrac{22}{44} = \dfrac{1}{2} \]