S = p/(q + p(1 − q)) solve for q
s = p/(q +p -pq)q +p -pq = p/sq -pq = p/s - pq(1-p) = p/s - pq = (p/s - p) / (1-p)
S = p/(q+p(1-q))
S(q+p(1-q)) = p
S(q+p-pq) = p
Sq+Sp-Spq = p
Sq-Spq = p-Sp
q(S-Sp) = p-Sp
q = (p-Sp)/(S-Sp)
