Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 322 / 1 / i / 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 givesThis is just under one percent of systems. Squaring the marginal single-star fraction would incorrectly give two independently sampled component ages.