It is known that 5% of the population has disease A, which can bediscovered by m

Question

It is known that 5% of the population has disease A, which can bediscovered by means of a blood test. Suppose that N (a largenumber) people are tested. The blood sample of k people arepooled together and analyzed. (Assume that N=nk, with n aninteger.) If the test is negative, all of the persons in thepool are healthy and only one test is needed. If the test ispositive, each of the k persons must be tested separately and atotal of k+1 tests are needed.

For a fixed k, what is the expected number of tests needed?

Explanation / Answer

[(0.95)k][1] +[1-(0.95)k][k+1] = (0.95)k + k + 1 -k(0.95)k - (0.95)k =[1-(0.95)k][k]+1
n{[1-(0.95)k][k]+1}

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.