Question

One bag contains $4$ white and $5$ black balls. Another bag contains $6$ white and $7$ black balls. A ball is transferred form first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn in white.

Answer 1

$A=$ Event that white ball transferred

$B=$ Event that black ball transferred

$C=$ Event that ball drawn from secondary bag is white

$\Rightarrow P$ ( ball drawn is white ) $=P$ ( white ball transferred ) $P$ ( Ball drawn white ) $+P$ ( black ball transferred ) $\times P$ ( ball drawn white )

$=\frac{4}{9}\times \frac{7}{14}+\frac{5}{9}\times \frac{6}{14}$

$=\frac{28+30}{126}$

$=\frac{58}{126}$

Hence, the answer is $\frac{58}{126}.$