Lung Cancer and SmokingDate: 10/20/2001 at 22:57:08 From: nin Subject: Probability Medical researchers know that the probability of getting lung cancer if a person smokes is .34. The probability that a nonsmoker will get lung cancer is .03. It is also known that 11% of the population smokes. What is the probability that a person with lung cancer will have been a smoker? Date: 10/21/2001 at 05:36:52 From: Doctor Mitteldorf Subject: Re: Probability Good question. Here's a clear way to think about it: Start by dividing the population into the 89% that doesn't smoke and the 11% that does. Now subdivide further: 89% times 0.03 is the probability of not smoking and getting lung cancer. 89% times 0.97 is the probability of not smoking and NOT getting lung cancer, etc. You can make a chart this way: Cancer No cancer Smokers | 3.74% | 7.26% | Non-smokers | 2.67% | 86.33% | --------- --------- Totals 6.41% 93.59% The question asks just about people with cancer, so our universe is just the first column. We can "re-scale" the probabilities to 100% by dividing both numbers by 6.41%, which is the total for the column: If a person has lung cancer, he has a probability 3.74/6.41 = 0.58 of being a smoker, and a probability 2.67/6.41 = 0.42 of being a non-smoker. (In the real world, I'm afraid more than 11% of people smoke, or have smoked, by the time they get to the age where lung cancer is tragically common. So in real life, a much larger majority of lung cancer patients are smokers or former smokers.) - Doctor Mitteldorf, The Math Forum http://mathforum.org/dr.math/ |
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