From a pack of 52 cards, a black jack, a red queen and two black kings fell down. A card was then drawn from the remaining pack at random. Find the probability that the card drawn is

(i) a black card

(ii) a king

(iii) a red queen.

Given, a black jack, a red queen and two black kings fell down.

Hence, remaining no. of cards = 52 - 4 = 48.

(i) There are total 26 black cards, 13 of club and 13 of spades. Out of which 3 are removed.

∴ No. of black cards left = 26 - 3 = 23.

P(a black card) = $\dfrac{23}{48}.$

Hence, the probability of drawing a black card is $\dfrac{23}{48}.$

(ii) There are total 4 kings, but 2 black kings are removed.

∴ No. of kings left = 4 - 2 = 2.

P(a king) = $\dfrac{2}{48} = \dfrac{1}{24}.$

Hence, the probability of drawing a king is $\dfrac{1}{24}.$

(iii) There are 2 red queens, one of hearts and one of diamonds.

Since, one red queen is removed, hence no. of red queens left = 2 - 1 = 1.

P(a red queen) = $\dfrac{1}{48}.$

Hence, the probability of drawing a red queen is $\dfrac{1}{48}.$