Application of Bayes' Thm.

Question

I know that for this problem you would use Bayes' Theorem, but I am having issues figuring out which pieces would be of value. So far I have:

P(cancer) = .008 P(accurate test given cancer) = .95 P(not accurate test given no cancer) = .07

And I am looking for:

P(accurate test given neg. test for cancer)

And from the thm. I have for Bayes', I do not have enough info (which I know is wrong). Can anybody see what I am messing up with?

Answer 1

The formula for Baye's theorem: http://en.wikipedia.org/wiki/Bayes'_theorem

$P$(Test is accurate|Positive for Cancer) = $\frac{P(Positive\ for\ Cancer|Test\ is\ accurate)*P(Test\ is\ accurate)}{P(Positive\ for\ Cancer)}$.

Now fill in the missing values.

P(Test is accurate) = $$(0.008)*(0.95) + (0.992)*(0.93)$$ P(Positive for Cancer) = $$(0.008)*(0.95) + (0.992)*(0.07)$$ P(Positive for Cancer|Test is accurate) = $$\frac{0.008*0.95}{(0.008)*(0.95) + (0.992)*(0.93)}$$