Paragraph: A box B₁ contains 1 white ball, 3 red balls and 2 black balls. Another box B₂ contains 2 white balls, 3 red balls and 4 black balls. A third box B₃ contains 3 white balls, 4 red balls and 5 black balls. Question: If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B₂ is

Step-by-step solution

Let A   : one ball is white and other is red E 1   : both balls are from box B 1 E 2   : both ball are from box B 2 E 3   : both ball are from box B 3 Hence, P required = P E 2 A = P A E 2 · P E 2 P A E 1 · P E 1 + P A E 2 · P E 2 + P A E 3 · P E 3 = 2 C 1 × 3 C 1 9 C 2 × 1 3 1 C 1 × 3 C 1 6 C 2 × 1 3 + 2 C 1 × 3 C 1 9 C 2 × 1 3 + 3 C 1 × 4 C 1 1 2 C 2 × 1 3 = 1 6 1 5 + 1 6 + 2 1 1 = 5 5 1 8 1