A test to determine whether a certain anybody is present is 99.2% effective. Thi

Question

A test to determine whether a certain anybody is present is 99.2% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.2% of the time. The probability of a test come back positive when the antibody is not present (a false positive) is 0.008. Suppose the test is given to five randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all five people? (b) What is the probability that the test comes back positive for at least one of the five people? (a) P(all 5 tests are negative) = (Round to four decimal places as needed.)

Explanation / Answer

a)

Supposing that the tests are independent then

P (all 5 tests are negative) = (0.992) *(0.992) *(0.992) *(0.992) *(0.992)

   =0.9606349

   (0.9606 four decimal places)

b)

This is just the complement of above

P (at least one of the 5tests positive) = 1 – P (all 5 have negative tests)

=1-0.9606349

   =0.039365099

     (0.0394 four decimal places)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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