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.

Assume that the patient keeps on trying the test, what is the minimum number of tests that the patient has to try to be 99% percent sure that he is actually ill? Assume that all tests are conducted independently.

math Statistics-And-Probability

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Answer 1

Answer #1

Probability of disease P(D) = 1/100000 =0.00001

and of not having disease = P(ND) = 1 - 0.00001

= 0.99999

Probability of positive test result, given person has disease = P(+ve|D ) = 0.99

Probability of positive test result, given person does not have disease = P(+ve|ND ) = 0.01

1) Probability for you to have the disease when you did two tests and both of them

show positive = 1-P(not having the disease)

= 1-(1-0.000989)*(1-0.000989)

= 0.001977

2) Let n be the number of tests,

hence probability of having disease with n test +ve = 1-(1-0.000989)ⁿ

= 0.99<1-(1-0.000989)ⁿ

= (0.999011)ⁿ < 0.01

= nln (0.999011) <ln(0.01)

n>4653.571

n = 4654

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Answer 2

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