= Solution
For the <evolved-companion fraction>, a <red giant> has another evolved component precisely for unordered $GG$ or $GW$ pairs. By <conditional independence> at fixed age, their combined slice <probability> is $g^2+2gw=9g^2$. Therefore
$$
\Pr(GG\text{ or }GW)=\int_0^1\frac{9y^2}{10000}\,dy=\frac9{30000}.
$$
Divide by the system fraction containing at least one <red giant> to obtain \b[the requested conditional fraction]:
$$
\boxed{\Pr(\text{another evolved component}\mid\text{at least one }G)=\frac9{299}\simeq3.01003\%.}
$$
A double-giant system is counted once in this denominator, and the factor two for a giant–<white dwarf> pair represents its two possible component orderings.
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