
And the answer is 0.0333 or a 1/3 and now we're going to

apply the entire arsenal of inference we just learned about.

The joint probability of cancer and positive is 0.1 * 0.9. That's the joint that's not normalized.

So let's normalize it and we normalize it by the sum of the joint

for cancer and the joint for noncancer.

Joint for cancer we just computed but the joint for noncancer assumes the opposite prior 10.1

and it applies the positive result of a noncancer case.

Now because the specificity first is negative, we have to do the

same trick as before and multiply it with 10.8.

When you worked this out, you find this to be 0 to 0.9 divided 0 to 0.9 + 0.9 * 0.2 that is 0.18

So if you put these all of this together, you get exactly a third.