What is the probability that the ball moved and the ball drawn are of the same colour?

Explanation

1. 01

   Both red: $\frac{3}{5} \times \frac{3}{6} = \frac{9}{30}$; both black: after a black ball moves in, bag II has 4 black balls of 6, so $\frac{2}{5} \times \frac{4}{6} = \frac{8}{30}$.

2. 02

   $\frac{9}{30} + \frac{8}{30} = \frac{17}{30}$.