Vivekanand Vellanki
0

The ball transferred from bag 1 to bag 2 is either red (event R) or black (event B).

Let P(BB) be the probability of picking a black ball from bag 2 after a ball has been transferred from bag 1 to bag 2.

P(BB) = P(R)*P(BB/R) + P(B)*P(BB/B)

P(BB) = \frac{3}{7}\cdot\frac{5}{10}+\frac{4}{7}\cdot\frac{6}{10}=\frac{\left(15+24\right)}{70}=\frac{39}{70}