Question

Find the probability of getting both red balls, when from a bag containing 5 red and 4 black balls, two balls are drawn, with replacement

Answer 1

The bag contains 5 red and 4 black balls.

i.e., 5 + 4 = 9 balls.

2 balls can be drawn from 9 balls with replacement in ⁹C₁ × ⁹C₁ ways.

∴ n(S) = ⁹C₁ × ⁹C₁ = 9 × 9 = 81

Let event A: Balls drawn are red.

2 red balls can be drawn from 5 red balls with replacement in ⁵C₁ × ⁵C₁ ways.

∴ n(A) = ⁵C₁ × ⁵C₁ = 5 × 5 = 25

∴ P(A) = `("n"("A"))/("n"("S"))`

= `25/81`