- #1
mathmari
Gold Member
MHB
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Hey!
We assume that for a particular illness, a doctor recommends a dangerous surgery if, after a clinical examination and by laboratory tests, he is 80% sure that his patient suffers from it, or, in other case, he recommends further costly examinations. Laboratory tests make a good diagnosis in 99% of cases for non-diabetics and in 70% of cases for diabetics.
After a clinical examination, the doctor is 60% sure that Mr Peter suffers from the disease. Laboratory tests that have a positive result (for the disease) are also done.
Will the doctor operate Mr. Peter, believing that Mr. Peter is not diabetic, or will he recommend further tests?
What will the doctor do if Mr. Peter after the results remembers that he is diabetic? Could you give me a hint how we could check that?
Let $x$ be the probability that the patient suffers from the disease.
In the first case we consider that Mr Peter is not diabetic. Then the probability that he is ill, believing that he is non-diabetic is equal to $0.99\cdot x+0.01\cdot (1-x)$ and this must be equal to the estimation of the docrot, i.e. $0.99\cdot x+0.01\cdot (1-x)=0.6$.
Is this correct?
At the case where Mr Peter remembers that he is diabetic, do we have that $0.7\cdot x+0.3\cdot (1-x)=0.6$ ? Or have I understood wrong the exercise statement? (Wondering)
We assume that for a particular illness, a doctor recommends a dangerous surgery if, after a clinical examination and by laboratory tests, he is 80% sure that his patient suffers from it, or, in other case, he recommends further costly examinations. Laboratory tests make a good diagnosis in 99% of cases for non-diabetics and in 70% of cases for diabetics.
After a clinical examination, the doctor is 60% sure that Mr Peter suffers from the disease. Laboratory tests that have a positive result (for the disease) are also done.
Will the doctor operate Mr. Peter, believing that Mr. Peter is not diabetic, or will he recommend further tests?
What will the doctor do if Mr. Peter after the results remembers that he is diabetic? Could you give me a hint how we could check that?
Let $x$ be the probability that the patient suffers from the disease.
In the first case we consider that Mr Peter is not diabetic. Then the probability that he is ill, believing that he is non-diabetic is equal to $0.99\cdot x+0.01\cdot (1-x)$ and this must be equal to the estimation of the docrot, i.e. $0.99\cdot x+0.01\cdot (1-x)=0.6$.
Is this correct?
At the case where Mr Peter remembers that he is diabetic, do we have that $0.7\cdot x+0.3\cdot (1-x)=0.6$ ? Or have I understood wrong the exercise statement? (Wondering)