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 makesa positive diagnosis}. Doctor A diagnoses 25% of all patients as positive, doctor Bdiagnoses 40% of all patients as positive, and both doctors diagnose 10% of allpatients as positive. Are the diagnoses of the two doctors independent? Suppose a patient is referred for further lab tests if either doctor A or Bmakes a positive diagnosis. What is the probability that a patient will be referredfor further lab tests?