Question

Two cards are drawn from a pack of 52 cards. Find the probability that one is club and the other is a diamond.

Answer 1

Two cards can be drawn from a pack of 52 cards in ⁵²C₂ = `(52 xx 51)/(1 xx 2)` = 26 × 51 ways

∴ n(S) = 26 × 51

Let B = the event that one is club and the other is a diamond.

One club can be drawn from 13 clubs in ¹³C₁ = 13 ways

Similarly, one diamond can be drawn in 13 ways

∴ one club and one diamond can be drawn in 13 × 13 ways

∴ n(B) = 13 × 13

∴ the reqwred probability= P(B) = `("n"("B"))/("n"("S"))`

= `(13 xx 13)/(26 xx 51)`

= `13/102`