When would $\Theta_{Bayes}$ be on the Equal Error Rate curve

If we use the classic Bayesian classification for a 2 class problem and classify based on comparing likelihood ratio $LR(x) = \frac{p(x|s=1)}{p(x|s=2)} $ to a $\Theta_{Bayes} = \frac{P(s=2)}{P(s=1)}$ when would this $\Theta_{Bayes}$ create equal false positive and false negative rates? My intuition is if classes have equal priors and $\Theta_{Bayes} = 1$. Is this the case?