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Applying Bayess rule, we have odds(smoker | cancer) = odds(smoker) * p(cancer | smoker) / p(cancer | non-smoker) Rearranging terms, we can solve for the risk ratio: p(cancer | smoker) / p(cancer | non-smoker) = odds(smoker | cancer) / odds(smoker) = 16 Thats the answer I had in mind, but let me address an objection raised by one poll respondent, who chose Other because, You cant draw casual inferences from observational data without certain assumptions which Im unwilling to make. Thats true

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