For a study on hypertension, people were classified as Non-smokers, Moderate Smokers or Heavy Smokers. The study found that 75% of people were Non-smokers,20% were Moderate Smokers and 5% were Heavy smokers. Of those classified as Non-smokers 30% had hypertension, of those classified as Moderate 58% had hypertension, and of those classified as Heavy smokers 61% had hypertension.
1. What proportion of all people have hypertension? (This uses multiplication rule of probability and total probability)
2. A doctor diagnosis a patient with hypertension, what is the probability that the patient is a Heavy Smoker? (This uses Bayes' Theorem, or you could use the definition of conditional, the multiplication rule and total probability)
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