From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random.
1) a face card (King, Jack or Queen)
2) an even-numbered red card
Solution
In a deck of 52 cards, for each suit, we have three cards with number 3, 6, 9 which are multiples of 3.
Thus for four different suits Spade, Heart, Diamond, Club, 3 × 4 = 12 such cards will be removed.
∴ Total number of outcomes = 52 – 12 = 40
1) Each suit has 3 face cards.
Four suits (Spade, Heart, Diamond, Club) will have 3 × 4 = 12 face cards.
So, the required probability will be given by
P(getting a face card) = `12/40 = 3/10`
2) Each suit has 4 (cards with number 2, 4, 8, 10) even numbered cards.
Heart and Diamond cards are of red colour
Thus, two suits will have 2 × 4 = 8 even numbered cards
So, the required probability would be given by
P(getting an even-numbered red card) = `8/40 = 1/5`
