You are diagnosed with an uncommon disease. You know that there only is a 1% chance of getting it. Use the letter D for the event "you have the disease and T for "the test says so." It is known that the test is imperfect: P(T|D)=0.98P(T|D)=0.98 and P(Tc|Dc)=0.95.P(Tc|Dc)=0.95. a. Given that you test positive, what is the probability that you really have the disease? Please show step by step explanation. Thank you.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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You are diagnosed with an uncommon disease. You know that there only is a 1% chance of getting it. Use the letter D for the event "you have the disease and T for "the test says so." It is known that the test is imperfect: P(T|D)=0.98P(T|D)=0.98 and P(Tc|Dc)=0.95.P(Tc|Dc)=0.95.

a. Given that you test positive, what is the probability that you really have the disease?

Please show step by step explanation. Thank you.

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