Three boxes B ₁, ~B ₂ and B ₃ contain balls with different colors as follows: array cccc & White & Black & Red B ₁ & 2 & 1 & 2 ~B ₂ & 3 & 2 & 4 ~B ₃ & 4 & 3 & 2 array A die is thrown. Box B₁ is chosen if either 1 or 2 turns up. Box B₂ is chosen if 3 or 4 turns up and box B₃ is chosen if 5 or 6 turns up. Having chosen a box in this way, a ball is drawn at random from that box. If the ball drawn is found to be Red, the

Step-by-step solution

If 1 or 2 turns up, box B₁ is selected Hence, P (B₁ )= 2 6 Similary, P ( B ₂ )= 2 6 and P ( B ₃ )= 2 6 For box B ₁ : Total number of balls =5 No. of red balls =2 Probability of red ball = 2 5 P ( R B₁ )= 2 5 Similarly, P ( R B ₂ )= 4 9 and P ( R B ₃ )= 2 9 Now, the required probability is P ( B₂ R )= P ( R B₂ ) P (B₂ ) P ( R B₁ ) P (B₁ )+P ( R B₂ ) P (B₂ )+P ( R B₃ ) P (B₃ ) = 4 9 2 6 2 6 2 5 + 4 9 2 6 + 2 9 2 6 = 5 12