Will the doctor operate the patient? 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? 
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Could you give me a hint how we could check that? 
Do we consider the haf percentage of the clinical examination and the half percentage of the results of the laboratory tests?  
 A: Let $x$ be the probability to suffer from the disease.  If a person suffers from the disease it will be considered ill with probability $0.7$, so from here $0.7x$ of all will be considered positive.  Additional one percent of the healthy persons will be wrongly considered positive, that is $0.01(1-x)$.  Hence in total
$$0.7x+0.01(1-x)$$ will be considered positive.  
This probability must equal the doctor’s estimation for that person to be positive, namely $0.6$. Now solve for $x$.
A: The question is not really particularly well phrased, as we don't really know what the doctor will do (it'd depend on how costly the test is and how "costly" operating on a healthy patient is). But we definitely can calculate the probability that the patient is sick.
Of course, there are two possibilities that the patient's result is positive, either he is sick and the result is true positive, or he is healthy and the result is a false positive.
You need to find the probability he is sick and he got a positive result, and the total probability of getting a positive result (so the previous probability plus the probability that he is healthy and he got a positive result). Then, you need to use Bayes' theorem to find the probability that he is sick, given that his result was positive. 
