Question

Two cards are drawn from a pack of 52 cards. Find the probability that both are from the same suit.

Answer 1

Two cards can be drawn from a pack of 52 cards in ⁵²C₂ ways.

∴ n(S) = ⁵²C₂ 

Let event  C: Both the cards are drawn are of the same suit.

A pack of 52 cards consists of 4 suits each containing 13 cards.

∴ 2 cards can be drawn from the same suit in ¹³C₂ ways.

∴ n(C) = ¹³C₂ × 4

∴ P(C) = `("n"("C"))/("n"("S"))`

= `(4 xx ""^13"C"_2)/(""^52"C"_2)`

= `(4 xx 13 xx 12)/(52 xx 51)`

= `12/51`