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.

Are the events A⁺, B⁺independent?

A.No, because P(A n B) is not equal to P(A) + P(B)

B.Yes, because P(A U B) is equal to P(A) + P(B)

C.No, because P(A n B) is not equal to P(A) * P(B)

D.Yes, because P(A n B) is equal to P(A) * P(B)