255.Heavy Smoker, Given Death
★★★conditional probabilitySIG
In a population, 50% do not smoke, 20% are light smokers and 30% are heavy smokers. A heavy smoker is twice as likely to die as a light smoker, and a light smoker is twice as likely to die as a non-smoker. Given that a person has died, what is the probability that they were a heavy smoker?
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Only relative death rates matter, so assign non-smokers a rate of 1 and scale from there. Weight each group by its size times its rate.
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