For k=1,2,3 the box B_k contains k red balls and (k+1) white balls. Let P (B₁ )= 1 2 , P (B₂ )= 1 3 and P (B₃ )= 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 fr

Question

For k=1,2,3 the box B_k contains k red balls and (k+1) white balls. Let P (B₁ )= 1 2 , P (B₂ )= 1 3 and P (B₃ )= 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 B₂ , is

Quantrex Academy · Accepted Answer

Correct answer: B. 14 39

In a box, aligned B₁ & =1 R, 2 W B₂ & =2 R, 3 W and B₃ & =3 R, 4 W aligned Also, given that, aligned & P (B₁ )= 1 2 , P (B₂ )= 1 3 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 & = 2 15 35+28+15 210 = 2 15 210 78 = 14 39 & aligned

For k=1,2,3 the box B_k contains k red balls and (k+1) white balls. Let P (B₁ )= 1 2 , P (B₂ )= 1 3 and P (B₃ )= 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 B₂ , is

Options

Correct answer

Step-by-step solution

More from Probability