(Laughter)

That means that is not giving any false positives or any false negatives.

The tests aren't a hundred percent accurate, but...

Well, amongst the 100 who do have the disease, the test will get it right 99 percent of the time, and 99 will test positive.

Amongst all these other people who don't have the disease, the test will get it right 99 percent of the time.

We can tell with absolute certainty that the person has cancer, and we can determine what the outcome of the test is.

The blood test is normal.

Well, that cow must have cheated on his test.

Here's another quiz for you now suppose we've got a test for a disease which isn't infallible, but it's pretty good.

(Laughter)

And what's the same for P( C, Neg).

Check

Inspection?

Analyze.

Let's assume the probability of the test coming out positive given that we don't have this cancer is 0.2.

less than one in 100 actually have the disease.

So, the test really helped us gaining confidence that we are cancer free.

Now comes the hard part

Beau, put your hand down. laughter and cheering

Which is the test they're going to run that will tell us whether or not Caster Semenya is male or female?

Can I look at the fast?

Now, that's a logical error.

Now, what's remarkable about this outcome is really what it means.

In our cancer example, we know that the prior probability of cancer is 0.01, which is the same as 1 .

Specifically, the joint probabilities.

The probability of a positive test and having cancer.

A biopsy.

The BinetSimon.

It's the inspection team.

Looks like the safety inspector.

Maybe we should check for safety.

So if you get a positive test result you're going to raise the probability of having cancer relative to the prior probability.

In this example, we again might have our unobservable cancer C, but now we're running 2 tests, test 1 and test 2.

And the answer is 0.45.

Recommendation 2

Oh, you're referring to the blood tests

I can't let them search me.

Now, let's do one last modification and let's write this procedure assuming you observed a negative test result.

There's a big clot in the middle of the artery.

What about ballistics?

Ballistics.

Do you have the results?

I'll test him again.

How's the blood?

Let's go the cancer example. These are prior probability of cancer we should call P₀.