= Solution
A system containing a <red giant> and another evolved component is either a giant–giant pair or an unordered giant–<white dwarf> pair. At common age $y$, these disjoint possibilities have conditional <probabilities> $g(y)^2$ and $2g(y)w(y)$. The <conditional evolved-companion fraction in a coeval binary population> therefore has numerator
$$
\Pr(GG\text{ or }GW)=\int_0^1\left(\frac{y^2}{10000}+\frac{2y^2}{2500}\right)dy
=\frac9{30000}.
$$
Divide by the fraction $299/30000$ of systems containing at least one giant:
$$
\boxed{\Pr(\text{another evolved component}\mid\text{at least one giant})=\frac9{299}=0.0301003\ldots.}
$$
Thus \b[just over $3\%$ of giant-containing binaries have an evolved companion]. The $0.03\%$ numerator is a fraction of all binaries; it is not itself the requested conditional fraction.
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