Question

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

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 D ≡ the event that both the cards are red cards

There are 26 red cards

∴ two red cards can be chosen in ²⁶C₂

= `(26xx25)/(1xx2)`

= 13 × 25 ways

∴ n(D) = 13 × 25

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

= `(13 xx 25)/(26 xx 51)`

= `25/102`