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This is approximately 0.0011, which we get by dividing 0.001 by the normalizer 0.892,
and the posterior probability of being cancer-free after the test
is approximately 0.9989, and that's obtained by dividing this probability over here by the normalizer
and not surprisingly, these two values indeed add up to 1.
Now, what's remarkable about this outcome is really what it means.
Before the test, we had a 1% chance of having cancer,
now, we have about a 0.9% chance of having cancer.
So, a cancer probability went down by about a factor of 9.
So, the test really helped us gaining confidence that we are cancer-free.
Conversely, before we had a 99% chance of being cancer free, now it's 99.89%.
So, all the numbers are working exactly how we expect them to work.