Solution
= Solution
At a fixed age, the <probability> that at least one component is a <red giant> is $1-(1-g)^2=2g-g^2$. Integrating over the common age in the <coeval binary population> gives
$$
\boxed{\Pr(\text{at least one }G)=\int_0^1\left(\frac{2y}{100}-\frac{y^2}{10000}\right)dy=\frac{299}{30000}=0.996\overline6\%.}
$$
This is \b[just under one percent of systems]. Squaring the marginal single-star fraction would incorrectly give two independently sampled component ages.