A box `B_1`, contains 1 white ball, 3 red balls and 2 black balls. Another box `B_2`, contains 2 white balls, 3 red balls and 4 black balls. A third b

Question

A box B 1 B , contains 1 white ball, 3 red balls and 2 black balls. Another box B 2 B , contains 2 white balls, 3 red balls and 4 black balls. A third box B 3 B , contains 3 white balls, 4 red balls and 5 black balls. A. 82 648 82 B. 90 648 90 C. 558 648 558 D. 566 648 566 Select the correct answer from above options

Answer 1

Correct Answer - A For i=1,2,3, let W i ( B i , R i ) W denote the event that the ball drawn from i t h i bag is white (black, red). ∴ ∴ Required probability = P { ( W 1 ∩ W 2 ∩ W 3 ) ∪ ( B 1 ∩ B 2 ∩ B 3 ) ∪ ( R 1 ∩ R 2 ∩ R 3 ) } = = P ( W 1 ∩ W 2 ∩ W 3 ) + P ( B 1 ∩ B 2 ∩ B 3 ) + P ( R 1 ∩ R 2 ∩ R 3 ) = = P ( W 1 ) P ( W 2 ) P ( W 3 ) + P ( B 1 ) P ( B 2 ) P ( B 3 ) + P ( R 1 ) P ( R 2 ) P ( R 3 ) = = 1 6 × 2 9 × 3 12 + 2 6 × 4 9 × 5 12 + 3 6 × 3 9 × 4 12 = 82 648 =