The ball drawn from bag II is red.

Explanation

1. 01

   Let $E_1$ be that the ball moved is red and $R$ that the ball drawn is red: $P(E_1)\,P(R \mid E_1) = \frac{3}{5} \times \frac{1}{2} = \frac{9}{30}$, and $P(R) = \frac{13}{30}$.

2. 02

   $P(E_1 \mid R) = \frac{9/30}{13/30} = \frac{9}{13}$.