There are n urns marked $1, 2, ..., n$ respectively, with each of the $n$ urns containing 4 white and 6 black balls. There is another urn, marked $(n+1)$ containing $5$ white and $5$ black balls. An urn is chosen at random from the $(n+1)$ urns, and two balls are drawn at random from that urn, both being black. The probability that $5$ white and $3$ black balls are left in the chosen urn is $1/7$. Determine that value of n.
I know I'm supposed to use Bayes' Rule to it, but I'm not sure how to categorize the events.