Q) One bag contains 4 white and 5 black balls. Another bag contains 6 white and 7 black balls. A ball is transferred from the first bag to the second bag. Find the probability that the ball drawn is white.

A) Prob. of white ball being transferred = 4/9

Prob. of black ball being transferred = 5/9

Prob. of white ball being drawn from 2nd bag ---->

Case 1. white transferred :

7 white 7 black so 1/2

Case 2. black transferred :

6 white 8 black so 6/14 = 3/7

Total Prob. = (4/9) (1/2) + (5/9)( 3/7)

= 2/9 + 5/21 = 14 + 15 / 63

= 29/63

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