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

Answer 1

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`