Problem source

A scientist is checking a sequence of microscope slides for cancerous
cells, marking each cancerous cell that she detects with a red dye.
The number of cancerous cells on a slide is random and has a Poisson
distribution with mean $\mu.$ The probability that the scientist
spots any one cancerous cell is $p$, and is independent of the probability
that she spots any other one. 
\begin{questionparts}
\item Show that the number of cancerous cells which she marks on a single
slide has a Poisson distribution of mean $p\mu.$ 
\item Show that the probability $Q$ that the second cancerous cell which
she marks is on the $k$th slide is given by 
\[
Q=\mathrm{e}^{-\mu p(k-1)}\left\{ (1+k\mu p)(1-\mathrm{e}^{-\mu p})-\mu p\right\} .
\]
\end{questionparts}