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Two cards are drawn from a pack of 52 cards. Find the probability that one is a face card and the other is an ace card - Mathematics and Statistics

Sum

Two cards are drawn from a pack of 52 cards. Find the probability that one is a face card and the other is an ace card

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Solution

Two cards can be drawn from a pack of 52 cards in 52C2 ways.

∴ n(S) = 52C2

Let event A: Out of the two cards drawn, one is a face card and the other is an ace card.

There are 12 face cards and 4 ace cards in a pack of 52 cards

∴ One face card can be drawn from 12 face cards in 12C1 ways and one ace card can be drawn from 4 ace cards in 4C1 ways.

∴ n(A) = 12C1 × 4C1

∴ P(A) = `("n"("A"))/("n"("S"))`

= `(""^12"C"_1 xx ""^4"C"_1)/(""^52"C"_2)`

= `(12 xx 4)/((52 xx 51)/(2 xx 1)`

= `8/221`

Concept: Concept of Probability
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