Making a Conditional Probability Chart

Date: 05/17/2000 at 14:44:08
From: Melisss Dolan
Subject: Probability

I have asked many math teachers to help me with this problem, and they 
can't figure it out, so I turn to you.

Medical records show that in a group of patients screened for lung 
cancer, 10% have the disease. Of those who have lung cancer, 93% are 
smokers. Of those who do not have lung cancer, 28% are smokers. If a 
person selected from this group is a smoker, what is the probability 
that the person has lung cancer?

Date: 05/18/2000 at 09:05:19
From: Doctor Anthony
Subject: Re: Probability

Making a chart:

               |Lung cancer    No lung cancer | Total
      ---------|------------------------------|-------
        Smoker |0.1 x 0.93       0.9 x 0.28   | 0.345
     Non-Smoker|0.1 x 0.07       0.9 x 0.72   | 0.655
      ---------|------------------------------|--------
       Total   |  0.1                0.9      | 1.00

 
 Given that a person is a smoker, the probability he has cancer

       0.1 x 0.93
     = ---------- = 0.26956
         0.345

- Doctor Anthony, The Math Forum
  http://mathforum.org/dr.math/