Hello, sf1903!
They are asking for: .
Given: .
What the probability that the paitent is ill and the test shows ill?
Using Bayes' Theorem on [2]: .
Substitute [1]: .
Therefore: .
A= the paitent is ill: P(A)=0,001
A*= the paitent is not ill
B= the diagnos shows ill
B*=the diagnos shows not ill
given: p(B|A)= 0,8
p(B*|A*)= 0,9
Question: What the probability that the paitent is ill and the diagnos shows ill?
started with: P(A|B)= P(A∩B)/P(B)= (P(A)xP(B|A))/P(B)
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