I am currently trying to solve problem which is formulated in the following way:
"An ectopic pregnancy is twice as likely to develop when the pregnant woman is a smoker as it is when she is a nonsmoker. If 32 percent of women of childbearing age are smokers, what percentage of women having ectopic pregnancies are smokers?"
which is conditional probability problem. Currently, I am stuck, as it appears I don't have enough information to solve the problem. The way I see it, problem requires me to find how is $P(E)$ divided between $P(E \cap S)$ and $P(E \cap \bar S)$, where $E$ is "woman have ectopic pregnancy" event, and $S$ is "woman smokes" event (I denote "woman do not smoke as $\bar S$). I can derive $$P(E) = P(E \cap S) + P(E \cap \bar S) = P(E|S)\cdot P(S) + P(E|\bar S)\cdot P(\bar S) = 2\cdot P(E|\bar S)\cdot P(S) + P(E|\bar S)\cdot P(\bar S) = 0.64 \cdot P(E|\bar S) + 0.68 \cdot P(E|\bar S)$$ but I have no idea how to go from there. There is not enough information to use Bayes formula, as I don't have any idea what $P(E)$ is. What am I missing in my thoughts?