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Question
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 an even numbered red card?
Solution 1
No. of total cards = 52
Cards removed of 4 colours of multiples of 3
= 3, 6, 9
= 4 × 3
= 12
Remaining cards = 52 – 12 = 40
An even number red cards = 2, 4, 8, 10 cards
= 2 × 4
= 8
`=>` Probability P(E) = `8/40 = 1/5`
Solution 2
The numbers which are multiples of 3 in 52 playing cards are 3, 6 and 9 i.e., 3 cards of each denomination.
∴ All cards whose numbers are multiples of 3 are = 4 × 3 = 12 cards ...(Jack, Queen and King of each denomination)
Remaining cards = 52 – 12 = 40
Now, Number of face cards = 12
P(even numbered red card) = `10/40 = 1/4`.
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