Question

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

Answer 1

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`