Bag B₁ contains 4 white and 2 black balls. Bag B₂ contains 3 white and 4 black balls. A bag is chosen at random and a ball is drawn from it at random, then the probability that the ball drawn is white, is

Step-by-step solution

Let P (B₁ ), P (B₂ ) and P(W) are the probabilty of selecting bag 1 , bag 2 and white bag respectively. P (B₁ )= 1 2 =P (B₂ ) aligned & P ( W B₁ )= 4 6 = 2 3 & P ( W B₂ )= 3 7 aligned Now, from the total probability theorem: aligned & P(W)=P ( W B₁ ) P (B₁ )+ P ( W B₂ ) P (B₂ ) & = 1 2 2 3 + 1 2 3 7 = 23 42 aligned