There is a rare disease that only happens to 1 out of 100,000 people. A test...

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There is a rare disease that only happens to 1 out of 100,000 people. A test shows positive 99% of times when applied to an ill patient and 1% of times when applied to a healthy patient. Please answer the following questions

What is the probability for you to have the disease when you did two tests and both of them show positive? Assume that two tests are conducted independent.

math Statistics-And-Probability

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Answer 1

Answer #1

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P(disease)=1/100000=0.00001

P(positive/disease)=0.99

P(positive/not disease)=0.01

P(positive)=P(positive/disease)*P(disease)+P(positive/not disease)*P(not disease)

=0.99*0.00001+0.01*(1-0.00001)=0.0100098

P(disease/positive)=P(positive/disease)*P(disease)/P(positive)

=0.99*0.00001/0.0100098=0.000989

As,both test are independent,so

P(disease/test 1 is positive and test 2 is positive)

=P(disease/test 1 is positive)*P(disease/test 2 is positive)

=0.000989*0.000989

=0.000001

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Answer 2

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