Just Selection

$\bar{f}(t) =$ average fitness of population at time $t$.
$m(s,t) =$ instances of schema $s$ in population at time $t$.
$\hat{u}(s,t) =$ average fitness of instances of $s$ at time $t$.
Probability of selecting $h$ in one selection step is \[ \array{ Pr(h) & = & \frac{f(h)}{\sum_{i=1}^{n} f(h_i)} \\ & = & \frac{f(h)}{n \bar{f}(t)} } \]
Probabilty of selecting an instance of $s$ in one step \[ \array{ \Pr(h \in s) & = & \sum_{h\in s \cap p_{t}} \frac{f(h)}{n \bar{f}(t)} \\ & = & \frac{\hat{u}(s,t)}{n \bar{f}(t)}m(s,t) } \]
Expected number of instances of $s$ after $n$ selections \[ \array{ E[m(s,t+1)] & = & \frac{\hat{u}(s,t)}{\bar{f}(t)}m(s,t) } \]