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
(iii) a black card
(iv) a heart
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
(iii) a black card
(iv) a heart

(iii) Let E be the event of getting a black card.

There will be 23 black cards remaining since 3 spades are removed.

Number of favourable outcomes = 23

P(E) = 23/49

Hence the probability of getting a black card is 23/49.

(iv) Let E be the event of getting a heart.

There will be 13 hearts.

Number of favourable outcomes = 13

P(E) = 13/49

Hence the probability of getting a heart is 13/49.