Reference no: EM132856330

1% of the population have a certain genetic defect.

a ) A test has been developed such that 90% of administered tests accurately detect the gene (true positives). What needs to be the false positive probability so that the probability of a patient having the genetic defect given a positive result (the posterior) is 90%?

For b)-d) consider the following. A test has been developed such that 1% of administered tests are positive when the patient doesn't have the gene (false positives).

b) What needs to be the true positive probability so that the probability of a patient having the genetic defect given a positive result (the posterior) is 50%?

c) Show that there is no true positive probability such that the probability of a patient having the genetic defect given a positive result (the posterior) can be 90%. (Hint: remember a probability p needs to fulfill 0 ≤ p ≤ 1.)

d) What is the highest posterior probability such a test can have? What is the corresponding true positive probability? (Hint: remember a probability p needs to fulfill 0 ≤ p ≤ 1.)