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Two cards are drawn from a pack of 52 cards. Find the probability that both are face cards. - Mathematics and Statistics

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Sum

Two cards are drawn from a pack of 52 cards. Find the probability that both are face cards.

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Solution

Two cards can be drawn from a pack of 52 cards in 52C2 ways.
∴ n(S) = 52C2
Let D be the event that both the cards drawn are face cards.

There are 12 face cards in a pack of 52 cards.
∴ 2 face cards can be drawn from 12 face cards in 12C2 ways
∴ n(D) = 12C2

∴ P(D) = `("n"("D"))/("n"("S"))`

= `(""^12"C"_2)/(""^52"C"_2)`

Concept: Elementary Properties of Probability
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