Answer to Question on Bayes

Answer to Question on Bayes:

Population experiences heart attacks: 20%

Smokers experience heart attacks : 90% (of all)

Without experience of a heart attack smokers: 60%

P(a|b) = L(b|a)P(a) / [ L(b|a)P(a) + L(b|not a)P( not a) ]

P(heart attack | smoker) = L(smoker | heart attack)Prior(heart attack) / [ L(smoker | heart attack)Prior(heart attack) + L(smoker | no heart attack)Prior(no heart attack) ]

P(heart attack | smoker) = (90% * 20%) / [ (90% * 20%) + (60% * 80%) ]

P(heart attack | smoker) = 27%