Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 42 / 3 / i

Condition on the common age $Y=y$ of the coeval binary population. Each component is a red giant with conditional probability $g(y)=y/100$, independently of the other component at that age. The conditional probability of at least one giant is $1-(1-g{)}^2=2g-g^2$. Integrating over the uniform age distribution givesThus the fraction is $299/30000=0.996\overline{6}\%$, just below $1\%$. The subtracted term removes the systems counted twice because both components are red giants. Using the square of the marginal giant fraction would incorrectly ignore their shared age.