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Let's go the cancer example. These are prior possibility of cancer we should call P₀.
This is a probability give a positive test given cancer. I call this P₁
and careful, these are probably a given negative test result for don't have cancer and I call this P₂.
Just to check suppose probability of cancer is 0.1, the sensitivity 0.9, specificity is 0.8.
Given the probability that a test will come out positive.
It's not Bayes rule yet, it's a simpler calculation and you should know exactly how to do this.