A box $B_1$ contains 1 white ball and 3 red balls. Another box $B_2$ contains 2 white balls and 3 red balls. If one ball is drawn at random from each of the boxes $B_1$ and $B_2$, then find the probability that the two balls drawn are of the same colour.

$\frac{11}{20}$

The correct answer is Option (2) → $\frac{11}{20}$ ##

$ ∴P(\text{Required}) = P(\text{Both are white}) + P(\text{Both are red})$

$= \left( \frac{1}{4} \times \frac{2}{5} \right) + \left( \frac{3}{4} \times \frac{3}{5} \right)$

$= \frac{2}{20} + \frac{9}{20} = \frac{11}{20}$