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

Question

A test to determine whether a certain antibody is present s 99.2% effective. This means that the test will accurately come back negative 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? b) What is the probability that the test comes back positive for at least one of the six people? (a) P(all 6 tests are negative) = (b) P(at least one positive) =

Explanation / Answer

Ans: Binomial distribution:

n=6

Probability of success,p i.e. test will come back negative=0.992

Probability of failure,1-p i.e. test will come back positive=1-0.992=0.008

a)Probability that test comes back negative for all six people=6C6*(0.992)6*(0.08)0 =1*0.9529*1=0.9529

b)Probability that test comes back positive for at least one of the six people

=1-P(test comes back positive for none of the six people)

=1-P(test comes back negative for all six people)

=1-0.9529

=0.0471

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