Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

An ectopic pregnancy is twice as likely to develop for a woman who is a smoker as opposed to nonsmoker. If 28% of women of childbearing age are smokers what percentage of ectopic pregnancies are smokers?

share|cite|improve this question
Hint: Work out $P(E)$ using the law of total probability $$P(E) = P(E\mid S)P(S)+P(E\mid S^c)P(S^c)$$ and the given fact that $P(E\mid S) = 2P(E \mid S^c)$. The answer will be a function of $P(E\mid S)$. Then use Bayes' formula $$P(S\mid E) = \frac{P(E\mid S)P(S)}{P(E\mid S)P(S)+P(E\mid S^c)P(S^c)}$$ and you will see that the unknown vaue of $P(E\mid S)$ will factor right out. – Dilip Sarwate Sep 29 '12 at 2:58

We assume that smokers are just as likely to get pregnant as non-smokers. This assumption is not necessarily reasonable, they may be too busy smoking to get pregnant. But without this kind of assumption we cannot solve the problem.

Let $E$ be the event "ectopic pregnancy," let $S$ be the event "smoker," and let $NS$ be the event "non-smoker." We have been asked to find the conditional probability $\Pr(S|E)$. By the usual formula we have $$\Pr(S|E)=\frac{\Pr(S\cap E}{\Pr(E)}.$$ Now we need to compute the probabilities on the right-hand side. Let $\Pr(E|NS)=p$. Then $\Pr(E|S)=2p$.

The event $E$ can happen in two disjoint ways: (i) the person is a smoker and has ectopic pregnancy or (ii) the person is a non-smoker and has an ectopic pregnancy.

The probability of (i) is $(0.28)(2p)$, and the probability of (ii) is $(0.72)(p)$. So $$\Pr(E)=(0.28)(2p)+(0.72)(p).\tag{$1$}$$ Easily, $\Pr(S\cap E)=(0.28)(2p)$.

Do the division asked for by Formula $(1)$. The $p$'s cancel.

share|cite|improve this answer
Thank u for walking thru. Very helpful. – kimj Sep 29 '12 at 4:50
@kimj: You pressed the spacebar before finishing your message. I get $43.75\%$. – André Nicolas Sep 29 '12 at 4:54

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.