\(P\left(\frac{W}{B_1}\right) = \frac14\)
\(P\left(\frac{R}{B_1}\right) = \frac34\)
\(P\left(\frac{W}{B_2}\right) = \frac25\)
\(P\left(\frac{R}{B_2}\right) = \frac35\)
Probability that both drawn ball from boxes B1 & B2 are of same colour
\(= P\left(\frac{W}{B_1}\right) P\left(\frac{W}{B_2}\right) + P\left(\frac{R}{B_1}\right) P\left(\frac{R}{B_2}\right)\)
\(= \frac 14 \times \frac 25 + \frac 34 \times \frac 35\)
\(= \frac2 {20 } + \frac 5 {20}\)
\(= \frac{11}{20}\)