lean_workbook_plus_81587

We are essentially being asked to compute $P(A|B)$ where $A$ is the assertion that the special ( $5$ white, $5$ black) urn was chosen, and $B$ is the assertion that both drawn balls are black. By Bayes' Theorem: $P(A|B)=\frac{P(B|A)P(A)}{P(B)}$ It is then fairly easily computed that: $P(B|A)=\frac{2}{9}$ , $P(A)=\frac{1}{n+1}$ , and $P(B)=\frac{2+3n}{9(n+1)}$ so $P(A|B)=\frac{2}{2+3n}$ . For this to equal $\frac{1}{7}$ requires $n=4$ . There seemed to be a missing backslash at least in the problem statement--which I corrected in quoting it.