Bag B 1 contains 6 white and 4 blue balls, Bag B 2 contains 4 white and 6 blue balls, and Bag B 3 contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn fro

Question

Bag B 1 ​ contains 6 white and 4 blue balls, Bag B 2 ​ contains 4 white and 6 blue balls, and Bag B 3 ​ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that the ball is drawn from Bag B 2 ​ , is :

TestHub · Accepted Answer

E 1 ​ : B a g B 1 ​ is selected B 1 ​ 6W4B ​ B 2 ​ 4 W 6 B ​ B 3 ​ 5 W 5 B ​ E 2 ​ : bag B 2 ​ is selected E 3 ​ : B a g B 3 ​ is selected A : Drawn ball is white We have to find P ( A E 2 ​ ​ ) P ( A E 2 ​ ​ ) = P ( E 1 ​ ) P ( E 1 ​ A ​ ) + P ( E 2 ​ ) P ( E 2 ​ A ​ ) + P ( E 3 ​ ) P ( E 3 ​ A ​ ) P ( E 2 ​ ) P ( E 2 ​ A ​ ) ​ ​ = 3 1 ​ × 10 6 ​ + 3 1 ​ × 10 4 ​ + 3 1 ​ × 10 5 ​ 3 1 ​ × 10 4 ​ ​ = 15 4 ​ ​

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