A test to determine whether a certain antibody is present is 99.1% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.1% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.009. 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?
Accepted Solution
A:
Answer:( a ) Probability that the test comes back negative for all four people = .9723( b ) Probability that t he test comes back positive for at least one of the four people = .0277Step-by-step explanation:GivenThe probability of the test will accurately come back negative if the antibody is not present = 99.1[tex]\%[/tex] = .991The probability of the test will accurately come back positive if the antibody is not present = .009Suppose the test is given to four randomly selected people who do not have the antibody .( a ) Probability that the test comes back negative for all four people = = [tex]991\times.991\times.991\times.991[/tex] = .9723If we say E = P( all 4 test are negative) or we say E = P( not of the all 4 test are positive) P( at least one of the 4 test are positive) = 1 - P( not of the all 4 test are positive) = 1 - P( all 4 test are negative)( b ) Probability that t he test comes back positive for at least one of the four people = 1 - P( all 4 test are negative) = 1 - .9723 = .0277