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Question
Two cards are drawn one after the other from a pack of 52 cards with replacement. What is the probability that both the cards drawn are face cards?
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Solution
Two cards are drawn from a pack of 52 cards with replacement.
n(S) = 52 × 52
Let A be the event that two cards drawn are face cards.
First card from 12 face cards is drawn with replacement in 12C1 = 12 ways
and second face card is drawn from 12 face card in 12C1 = 12 ways after replacement.
∴ n(A) = 12 × 12
∴ P (that both the cards drawn are face cards)
= P(A) = `("n"("A"))/("n"("S")`
= `(12xx12)/(52xx52)`
= `9/169`
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