Suppose two doctors, A and B, test all patients coming into a clinic for syphili

Question

Suppose two doctors, A and B, test all patients coming into a clinic for syphilis. Let events A^+ = {doctor A makes a positive diagnosis} and B^+ = {doctor B makes a positive diagnosis}. Suppose doctor A diagnoses 10% of all patients as positive, doctor B diagnoses 17% of all patients as positive, and both doctors diagnose 8% of all patients as positive. a. Are the events A^+, B^+ independent? Suppose a patient is referred for further lab tests if either doctor A or B makes a positive diagnosis. b. What is the probability that a patient will be referred for further lab test?

Explanation / Answer

a) Pr(A+) = 0.1, Pr(B+) = 0.17, Pr(A+ B+) = 0.08

Thus Pr(A+ B+) = 0.08 > Pr(A+) * Pr(B+) = 0.1 * 0.17 = 0.017.

The events are dependent. There is a similarity between how two doctors diagnose patients for sypilis

The previous formula used was P(A)*P(B) = Pr(A B) (TRUE for independent events)

b) The union of the 2 outcomes are required.

Pr(A+ B+) = Pr(A+) + Pr(B+) - Pr(A+ B+) = 0.1 + 0.17 – 0.08 = 0.19

Thus 19% of all patients will be referred for further lab tests

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