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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
Solution
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`
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