Question

One bag contains $4$ white and $5$ black balls. Another bag contains $6$ white and $7$ black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from second bag. If the probability that the ball drawn is white $\frac{29}{m}$.Find $m$

Answer 1

First bag- 4 white ,5 black

Second bag- 6 white ,7 black

A ball is transferred from first to second bag

case I) Transferred ball is white than in second bag 7 white 7 black

Probability that transferred ball is white ball from first bag=4/9

Probability that white ball is drawn from second ball=(7/14)*(4/9)=28/126

case II) Transferred ball is black than in second bag 6 white 8 black

Probability that transferred ball is black ball from first bag=5/9

Probability that white ball is drawn from second ball=(6/14)*(5/9)=30/126

Total probability=28/126+30/126=58/126=29/63

Therefore m=63