Problem No. 11. Urns and balls

There are 7 urns with 30 balls each. In each urn there is equal number of white and black balls. Randomly, we take out one ball from the first urn and put it into the second urn. Then, we take one ball from the second urn and put it into the third urn. We continue this process, until we take a ball from the seventh urn and put it into the first urn. Then, we take a ball from the first urn. What are the chances that the ball is black?

Student tip

First, find the probabilities for taking a black ball from each urn in first 7 steps.