Maharashtra State BoardHSC Science (Electronics) 11th
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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 - Mathematics and Statistics

Sum

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

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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 31)/(2 xx 1)`

= `13/34`

Concept: Concept of Probability
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