Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 322 / 1 / ii / 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 $g^2+2gw=9g^2$. ThereforeDivide by the system fraction containing at least one red giant to obtain the requested conditional fraction: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.