Question

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

Answer 1

Two cards can be drawn from a pack of 52 cards in ⁵²C₂ ways.
∴ n(S) = ⁵²C₂

Let A be the event that both the cards drawn are black.
The pack of 52 cards contains 26 black cards.
∴ 2 cards can be drawn from them in ²⁶C₂ ways
∴ n(A) = ²⁶C₂

∴ P(A) = `("n"("A"))/("n"("S"))`

= `(""^26"C"_2)/(""^52"C"_2)`