Question

A bag contains 6 black and 3 white balls. Another bag contains 5 black and 4 white balls. If one ball is drawn from each bag, find the probability that these two balls are of the same colour.

Answer 1

$$\begin{gathered} \text{Given:} \\ \text{Bag 1=}\left(\text{3W+6B}\right)\text{balls} \\ \text{Bag 2=}\left(\text{5B+4W}\right)\mathrm{balls} \\ P\left(\text{balls of same colour are drawn}\right)=P\left(\text{both black}\right)+P\left(\text{both white}\right) \\ =\frac{6}{9}\times \frac{5}{9}+\frac{3}{9}\times \frac{4}{9} \\ =\frac{30}{81}+\frac{12}{81} \\ =\frac{42}{81} \\ =\frac{14}{27} \end{gathered}$$