Question

A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.

Answer 1

Here, $W_1$ = {4 while balls} and $B_1$ = {5 black balls}

and $W_2$= {9 white balls} and $B_2$ = {7 black balls}

Let $E_1$ is the event that ball transferred from the first bag is white and E2 is the event that the ball transferred from the first bag is black.

Also, E is the event that the ball drawn from the second bag is white.
$\therefore P\left(\frac{E}{E_1}\right)=\frac{10}{17},P\left(\frac{E}{E_2}\right)=\frac{9}{17}$
and $P\left(E_1\right)=\frac{4}{9}andP\left(E_2\right)=\frac{5}{9}\therefore P\left(E\right)=P\left(E_1\right).P\left(\frac{E}{E_1}\right)+P\left(E_2\right).P\left(\frac{E}{E_2}\right)=\frac{4}{9}.\frac{10}{17}+\frac{5}{9}.\frac{9}{17}=\frac{40+45}{153}=\frac{85}{153}=\frac{5}{9}$