Question

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

(i) a black face card (ii) a queen (iii) a black card.

Answer 1

Total number of cards $=52$

Given that $3$ face cards of spades are removed.

Remaining number of cards $=52-3=49$

Number of possible outcomes, $n\left(S\right)=49$

Step $\mathbf{1}$: Find the probability of getting a black face card.

All the three face cards of spades are removed. Spade is black in colour.

Let $E$ be the event of drawing black face card.

Number of black face card left, $n\left(E\right)=3$ (face cards of club)

The probability of getting a black face card $=\frac{n\left(E\right)}{n\left(S\right)}=\frac{\mathbf{3}}{\mathbf{49}}$

Step $\mathbf{2}$: Find the probability of getting a queen.

Number of queen cards left $=3$

Let $E$ be the event of drawing queen cards.

$n\left(E\right)=3$

The probability of drawing queen card $=\frac{n\left(E\right)}{n\left(S\right)}=\frac{\mathbf{3}}{\mathbf{49}}$

Step $\mathbf{3}$: Find the probability of getting a black card.

Total number of black cards $=26$

All the three face cards of spades are removed.

Let $E$ be the event of drawing black card.

Remaining number of black cards, $n\left(E\right)=26–3=23$ ($13$ club $+10$ spade)

The probability of getting a black card $=\frac{n\left(E\right)}{n\left(S\right)}=\frac{\mathbf{23}}{\mathbf{49}}$