A study of residents of a region showed that 20% were smokers. The probability of death due to lung cancer, given that a person smoked, was ten times the probability due to lung cancer, given that the person did not smoke. If the probability of death due to lung cancer in the region is 0.006, what is the probability of death due to lung cancer given that the person is a smoker? Let S be the event the person smokes, let L be the event that a person dies due to lung cancer.
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For the region, the probability of death independently of the smoking status, is 0,6%. Let's say x is the probability of a non-smoker to die due to LC. Then, a smoker would have 10x. So, beacuse 20% of the residents smoke, for a representative portion of the region's population, numbering 100 people, it is true that: 0,6 = x*80 + 10x*20 0,6 = 80x + 200x 0,6 = 280x x = 0,6/280 = ~0,0214 So, the probability of a smoker is x*10 = 0,214.
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