= Solution
This is the <waiting time to observe both Bernoulli outcomes>. Write $q=1-p$, and let $S$ record the sex of the first captured animal. That first capture is always needed. If $S$ is male, every subsequent trial independently produces the required female with <probability> $q$, so $N-1$ has a <geometric distribution> with parameter $q$. If $S$ is female, $N-1$ has a <geometric distribution> with parameter $p$. By the <law of total expectation>,
$$
EN=1+p\frac1q+q\frac1p.
$$
Since $p+q=1$, this simplifies to \b[$\boxed{EN=1/(pq)-1}$], or
$$
\boxed{EN=\frac1{p(1-p)}-1.}
$$
The <expectation> includes both the first capture and the final capture completing the pair.
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