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Mr.Smith at age 35 has just gone through annual medical examination. The doctor tells him the...

Mr.Smith at age 35 has just gone through annual medical examination. The doctor tells him the bad news that he is tested positive for a serious disease and the test is rather accurate, 99% (the probability of testing positive given one gets the disease and also the probability of negative testing given one does not have the disease. On the contrary, the good news is that this disease is rare and just 0.01% of chances to get on average. What is the probability for Mr.Smith to indeed get such a disease?

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