A test to determine whether a certain antibody is present is 99.2 % effective. T

Question

A test to determine whether a certain antibody 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 coming back positive when the antibody is not present (a false positive) is 0.008. Suppose the test is given to six randomly selected people who do not have the antibody.

(a) What is the probability that the test comes back negative for all six people? P(all 6 tests are negative) (Round to four decimal places as needed.)

(b) What is the probability that the test comes back positive for at least one of the six people? P (at least one positive) (Round to four decimal places as needed.)

Explanation / Answer

Ans:

a)

First, testing each individual is an independent event, because knowing the results of the test for one person gives us no information about what the result will be for the next person. Therefore:

P (all 6 tests are negative) = (0.992)* (0.992)* (0.992)*(0.992)*(0.992)*(0.992)
= (0.992)6
0.9529

b)P(atleast positive for one of the six)=1-P(none of them positive)

=1-P(all negative)=1-0.9926=0.0471

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