Problem source

A bag contains $b$ black balls and $w$ white balls. Balls are drawn
at random from the bag and when a white ball is drawn it is put aside.
\begin{questionparts}
\item If the black balls drawn are also put aside, find an
expression for the expected number of black balls that have been drawn
when the last white ball is removed.
\item  If instead the black balls drawn are put back  into the bag,
prove that the expected number of times a black ball has been drawn when
the first  white ball is removed is $b/w\,$. Hence write down, in the form of
a sum,  an expression for the expected number of times a black ball has been drawn when
the last  white ball is removed.
\end{questionparts}