From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is

(i) a face card (King, Jack or Queen)

(ii) an even numbered red card ?

Cards whose numbers are multiples of 3 are : 3, 6 and 9 of each heart, club, diamonds and spades.

No. of cards removed = 3 × 4 = 12.

Total cards left = 40 (52 - 12).

∴ No. of possible outcomes = 40.

(i) There are 12 face cards in a deck of 52 playing cards.

∴ No. of favourable outcomes = 12.

P(drawing a face card) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{12}{40} = \dfrac{3}{10}$.

Hence, the probability that the card drawn is a face card = $\dfrac{3}{10}$.

(ii) Favourable outcomes (for an even numbered red card) are 2, 4, 8, 10 of heart and diamond.

∴ No. of favourable outcomes = 8.

P(drawing an even numbered red card)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{8}{40} = \dfrac{1}{5}$.

Hence, the probability that the card drawn is an even numbered red card = $\dfrac{1}{5}$.