Question

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. A. 116 181 B. 126 181 C. 65 181 D. 55 181 Select the correct answer from above options

Answer 1

Correct Answer - D Let E i ( i = 1 , 2 , 3 ) E denote the event of selecting i t h i bag and A denote the event of drawing one white and one red ball. Then, P ( E 1 ) = P ( E 2 ) = P ( E 3 ) = 1 3 P P ( A / E 1 ) = 1 6 × 3 6 + 3 6 × 1 5 = 1 5 P P ( A E 2 ) = 2 9 × 3 8 + 3 9 × 2 8 = 1 6 P P ( A / E 3 ) = 3 12 × 4 11 + 4 12 × 3 11 = 2 11 P Required probability = P ( E 2 / A ) = = P ( E 2 ) P ( A / E 2 ) P ( E 1 ) P ( A / E 1 ) + P ( E 2 ) P ( A / E 2 ) + P ( E 3 ) P ( A / E 3 ) = 1 3 × 1 6 1 3 × 1 5 + 1 3 × 1 6 + 1 3 × 2 11 = 55 181 1