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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 - Mathematics

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

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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`

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