Frorn 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 ?

Explanation

Cards bearing numbers 2, 3, 4, 5, 6, 7, 8, 9 and 10 are numbered cards in the pack of 52 playing cards.
The cards whose numbers are multiples of 3 are 3, 6 and 9.
As each suit has one '3', one '6' and one '9', therefore, in total we have four 3's, four 6's and four 9's.
`therefore` Total number of cards whose numbers are multiples of 3 = 12.
On removing these cards from the pack, the number of cards left in the pack = 52 - 12 = 40.
(i) As each suit has one king, one queen and one jack, therefore, in total we have 4 kings, 4 queens and 4 jacks.
`therefore` Total number of face cards in the pack = 12.
`therefore` The number of outcomes favourable to the event 'a face card' = 12.
`therefore" Probability (a face card) "=(12)/(40)=(3)/(10).`
(ii) Even numbered red cards left in the pack are 2, 4, 8, 10 of hearts and 2, 4, 8, 10 of diamonds.
`therefore` Total number of even numbered red cards in the remaining pack = 8.
`therefore` The number of outcomes favourable to the event 'an even numbered red card'= 8.
`therefore" P (an even numbered red card) "=(8)/(40)=(1)/(5).`