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In: Statistics and Probability

"A test to determine whether a certain antibody is present is 99.6​% effective. This means that...

"A test to determine whether a certain antibody is present is 99.6​% effective. This means that the test will accurately come back negative if the antibody is not present​ (in the test​ subject) 99.6​% of the time. The probability of a test coming back positive when the antibody is not present​ (a false​ positive) is 0.004. 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?"

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Expert Solution

the test will accurately come back negative if the antibody is not present​ (in the test​ subject) 99.6​% of the time. This is same as the probability that a test comes back negative given that the antibody is not present​ is 0.996

The probability of a test coming back positive when the antibody is not present​ (a false​ positive) is 0.004.

the test is given to five randomly selected people who do not have the antibody.

a) The probability that the test comes back negative given that the person does not have the antibody is 0.996

That means the probability that the test comes back negative for the 1st person = the probability that the test comes back negative for the 2nd person=...=the probability that the test comes back negative for the 5th person = 0.996 as all the 5 do not have antibody

the probability that the test comes back negative for all five ​people is

ans: the probability that the test comes back negative for all five ​people is 0.9802

b) the probability that the test comes back positive for at least one of the five ​people is

ans: the probability that the test comes back positive for at least one of the five ​people is 0.0198

orchestra answered 1 year ago
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