Let me test total probability in a quiz.

The probability of receiving a positive test result for either test is 0.9.

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What is the probability of a positive test result?

The probability of a positive test and having cancer.

This is a probability of a positive test given cancer.

Given the probability that a test will come out positive.

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That's an increased probability to the default probability, which we calculated before, which is the probability of any test, test 2 come in as positive before was the normalizer of Bayes rule which was 0.207.

The probability that the test triggers positive if you have cancer is 0.8, and the probability that the test comes out positive given that I'm cancer free is only 0.1.

My second test, after seeing a positive test, has now an increased probability of about 23 of coming in positive.

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This thing over here is the same as probability of test 2 to be positive, which I'm going to abbreviate with a 2 over here, conditioned on test 1 being positive and me having cancer times the probability of me having cancer given test 1 was positive plus the probability of test 2 being positive conditioned on test 1 being positive and me not having cancer times the probability of me not having cancer given that test 1 is positive.

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

So here before training, that's the pre, there's no difference in the performance score. That's the intelligence test.

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When you receive, say, a positive test result, what you do is, you take your prior P(C) you multiply in the probability of this test result, given C, and you multiply in the probability of the test result given (Neg_BAR_ C).

So, the additional information of a positive test only erased my posterior probability to 0.043.

The probability of a negative test and having cancer, and this is not conditional anymore.

And now finally tell me what is posterior probability of cancer given that we know we had a negative test result and the probability of negative cancer given there is a negative test result.

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Pre money was 15.

It's called pre death.

The other pre dough that we make is fermented our pre ferment.

And, again, the dependant variable's IQ changed, the difference between the score on the IQ test post training versus pre training.

Can you compute for me the probability of cancer given that I just received a positive test.

It's minus P of C Times the probability of getting a positive test result given not C.

There's some sort of a prior, of which we mean the probability before you run a test, and then you get some evidence from the test itself. and that all leads you to what's called a posterior probability.

What I want you to compute for me is the probability of the second test to be positive if we know that the first test was positive.

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