Question

Let R_i be the event of drawing read ball in ith draw and B_i be the event of drawing black ball
in ith draw.
Now, In bag there are 4R and 6B balls
$\therefore$ P(R₁) = $\frac{4}{10}$ and P(B₁) = $\frac{6}{10}$
Now according to given information
$P\left(\frac{R_2}{R_1}\right)=\frac{6}{12}and P\left(\frac{B_2}{B_1}\right)=\frac{4}{12}$
Required probabiflity
= P(R₁) $P\left(\frac{R_2}{R_1}\right)$ + P(B₁) $P\left(\frac{R_1}{B_1}\right)$
$=\frac{4}{10}\times \frac{6}{12}\times \frac{6}{10}\times \frac{4}{12}$
$=\frac{2}{5}$