For k=1,2,3 the box B _ k contains k red balls and (k+1) white balls. Let P ( B ₁ )= 1 2 , P ( B ₂ )= 1 3 and P ( B ₃ )= 1 6 . A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has

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For k=1,2,3 the box B _ k contains k red balls and (k+1) white balls. Let P ( B ₁ )= 1 2 , P ( B ₂ )= 1 3 and P ( B ₃ )= 1 6 . A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box B ₂, is

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Correct answer: B. 14 39

In a box, B₁=1 R, 2 W ; B₂=2 R, 3 W and B₃=3 R, 4 W Also, given that, P ( B ₁ )= 1 2 , P ( B ₂ )= 1 3 aligned & and P (B₃ )= 1 6 & P ( B₂ R )= P (B₂ ) P ( R B₂ ) P (B₁ ) P ( R B₁ )+P (B₂ ) P ( R B₂ )+P (B₃ ) P ( R B₃ ) =& 1 3 2 5 1 2 1 3 + 1 3 2 5 + 1 6 3 7 = 2 15 1 6 + 2 15 + 1 14 = 14 39 . aligned

For k=1,2,3 the box B _ k contains k red balls and (k+1) white balls. Let P ( B ₁ )= 1 2 , P ( B ₂ )= 1 3 and P ( B ₃ )= 1 6 . A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box B ₂, is

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