A diagnosis for a test is such that it (correctly) detects the disease in 87.5%

Question

A diagnosis for a test is such that it (correctly) detects the disease in 87.5% of the individuals who actually have the disease. Also, if a person does not have the disease, the test will report that he or she does not have it with probability 0.85. Only 1.5% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that he has the disease, what is the conditional probability that he does, in fact, have the disease?

Please type answer and include working.

Explanation / Answer

here let probabilty of test postive =P(TP) and probabilty of havinf disease =P(D) and not having =P(ND)

therefore probabilty of test postive =P(TP) =P(D)*P(TP|D)+P(ND)*P(TP|ND)

=0.015*0.875+(1-0.015)*(1-0.85)=0.160875

hence onditional probability that he does, in fact, have the disease=P(D|TP)=P(D)*P(TP|D)/P(TP)

=0.015*0.875/0.160875=0.081585

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.