The probability that a person has a certain disease is 002. Medical diagnostic t

Question

The probability that a person has a certain disease is 002. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.92. If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.01 a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present? b· If the medical diagnostic test has given a negative result (indicating that the disease is not present what is the probability that the disease is not present

Explanation / Answer

a)P(positive test)=P(have disease and test positive)+P(not have disease and test positive)

=0.02*0.92+(1-0.02)*0.01=0.0282

hence P(have disease given positive test result)=P(have disease and test positive)/P(posiitve test)

=0.02*0.92/0.0282=0.6525

b)

P(negative result)=1-P(positive result)=1-0.0282=0.9718

P(not have disease given negative result)=P(not have disease and test negative)/P(negaitve test)

=(1-0.02)*(1-0.01)/0.9718=0.9984

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