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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?

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    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.2012-09-29

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