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Question
Two cards are drawn from a pack of 52 cards. Find the probability that one is a heart card and the other is a non-heart card
Solution
Two cards can be drawn from a pack of 52 cards in 52C2 ways.
∴ n(S) = 52C2
Let event E: Out of the two cards drawn, one is the heart and the other is non-heart.
There are 13 heart cards in a pack of 52 cards, i.e., 39 cards are non-heart
∴ One heart card can be drawn from 13 heart cards in 13C1 ways and one non-heart card can be drawn from 39 cards in 39C1 ways.
∴ n(E) = 13C1 × 39C1
∴ P(E) = `("n"("E"))/("n"("S"))`
= `(""^13"C"_1 xx ""^39"C"_1)/(""^52"C"_2)`
= `(13 xx 39)/((52 xx 51)/(2 xx 1)`
= `13/34`
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