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Ten percent of a population suffers from a serious disease. A person suspected of the disease...

Ten percent of a population suffers from a serious disease. A person suspected of the disease is given two independent tests. Each test makes a correct diagnosis 90% of the  time. Find the probability that the person really has the illness a. given that both tests are positive or b. given that only one test is positive.

PLEASE DON'T JUST PROVIDE THE NUMBERS, PLEASE INCLUDE THE FORMULAS YOU ARE USING AND YOUR REASONING IF POSSIBLE!

Math   Statistics-And-Probability   
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