Suppose we have three urns with black and white balls distributed as follows:

Urn A has $10$ black balls and $20$ white balls
Urn B has $10$ black balls and $10$ white balls
Urn C has $10$ black balls and $1$ white ball.
Suppose we choose an urn (uniformly at random) and draw a ball (uniformly at random) from that urn. What is the probability that the ball is white?

I believe the answer is 
$$\frac{1}{3} \cdot \frac{2}{3} + \frac{1}{3} \cdot \frac{1}{2} + \frac{1}{3} \cdot \frac{1}{11}$$
Is that correct?