 Coeval binary population

A coeval binary has components formed at the same time. A population of such binary stars can still have a distribution of system ages. If component masses have independence and the state at age $t$ is determined separately for each component, the states have conditional independence given $t$. If $g(t)$ and $w(t)$ are the conditional probabilities of two states, the unconditional unordered pair fractions are $\mathbb{E}[g(t{)}^2]$ and $2\mathbb{E}[g(t)w(t)]$, not generally products of marginal state fractions.