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Putting all of this into mathematical notation
we've given the probability of having cancer
and from there, it follows the probability of not having cancer.
And they give me 2 conditional probability
that are the test being positive.
If we have have cancer, from which we can now predict the probability
of the test being negative of having cancer.
And the probability of the test being positive can be cancer free
which can complete the probability of
a negative test result in the cancer-free case.
So these things are just easily inferred
by the 1 minus rule.
Then when we read this,
you complete the probability of a positive test result
as the sum of
a positive test result given cancer
times the probability of cancer,
which is our truth table entry for the combination of P and C
plus the same given we don't have of cancer.
Now this notation is confusing and complicated
if we ever dive deep into probability, that's called
total probability,
but it's useful to know that this is
very, very intuitive
and to further develop intuition let me just give you
another exercise of exactly the same type.