agnostic test is used to screen subjects for Condition A. The test has sensitiei

Question

agnostic test is used to screen subjects for Condition A. The test has sensitieity Condition A with probability 0.98 0.98; that is, the test will declare a subject positive for when the subject is truly positive. The same test has specificity 0.90 that is, the test will declare a subject negative for Condition A with probability 0.90 when the subject is truly negative. The proportion of subjects in the population with Condition A is.O1 (a) Suppose that a randomly selected subject tests negative. What is the probability s/he is truly positive? Hint: Use Bayes Rule. (b) Suppose that n 100 randomly selected subjects from this population test negative. What is the probability that at least one of the subjects is truly positive? Assume that n -100 subjects are independent and use your probability p from part (a) vtn flip) , 0,7 PAGE 3

Explanation / Answer

a)P(test negative)=P(have condition and test negative+not have condition and test negative)

=0.1*(1-0.98)+(1-0.1)*0.9=0.812

hence P(true positive|test negative) =P(have condition and test negative)/P(test negative)=0.1*(1-0.98)/0.812

=0.002463

b)

P(at least one subject is true posiitve) =1-P(none of them is true posiitve) =1-(1-0.002463)100 =0.218554

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