Comment 63 by Martin Torp Dahl :

What is the probability that a women that tests positive for cancer on a mammography test actually has cancer given these numbers:

the probability that a woman has breast cancer is: 0.8 % (prevalence)

If a woman has breast cancer the chance of a positive test is 90% (sensitivity)

If a woman does not have breast cancer the probability of a positive test is 7% (specificity)

If nobody answers i guess i will give it, but it would be interesting to see if people here can figure it out.

Give it a try folks (give estimates, i don't expect perfect answers)

P(Cancer) = 0.008

P(~Cancer) = 0.992

P(Cancer | +) = 0.008 x 0.9 = 0.0072

P(Cancer | -) = 0.008 x 0.1 = 0.0008

P(~Cancer | +) = 0.992 x 0.07 = 0.06944

P(~Cancer | -) = 0.992 x 0.93 = 0.92256

=> P(+) = 0.0072 + 0.06944 = 0.07664

P(Cancer | +) / P(+) = 0.0072 / 0.07664 ~= 94%

Not easy to do in your head, which I guess is your point.