From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is :

(i) a black card

(ii) 8 of red colour

(iii) a king of black colour.

There are 12 face cards in a deck.

Remaining cards = 40 (52 - 12)

No. of possible outcomes = 40.

(i) There are 26 black cards in a deck.

Since, face cards are removed and there are 6 black face cards (a king, queen and jack of both club and spades).

No. of black cards left = 26 - 6 = 20.

∴ No. of favourable outcomes = 20.

P(drawing a black card) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{20}{40} = \dfrac{1}{2}$.

Hence, the probability of drawing a black card = $\dfrac{1}{2}$.

(ii) There are 2 number 8 red cards (1 of each heart and diamond).

∴ No. of favourable outcomes = 2.

P(drawing a 8 of red colour) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{2}{40} = \dfrac{1}{20}$.

Hence, the probability of drawing a 8 of red colour = $\dfrac{1}{20}$.

(iii) There is no king left as all face cards are removed.

∴ No. of favourable outcomes = 0.

P(drawing a king of black colour) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{0}{40}$ = 0.

Hence, the probability of drawing a king of black colour = 0.