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

We have,

Total number of cards = 52

If 3 face cards of spades are removed

Then, the remaining cards = 49 (52 - 3)

∴ Number of possible outcomes = 49.

(i) There are 3 black face cards of club left.

∴ Number of favourable outcomes = 3.

P(drawing a black face card) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{49}$.

Hence, the probability of drawing a black face card = $\dfrac{3}{49}$

(ii) There are total 4 queens and queen of spade is removed.

Queens left = 3

∴ Number of favourable outcomes = 3.

P(drawing a queen) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{49}$.

Hence, the probability of drawing a queen = $\dfrac{3}{49}$.

(iii) There are 26 black cards and 3 cards of spades are removed which are black.

Number of black cards left = 23 (26 - 3)

∴ Number of favourable outcomes = 23.

P(drawing a black card) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{23}{49}$.

Hence, the probability of drawing a black card = $\dfrac{23}{49}$.