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A test to determine whether a certain antibody is present is 99.4% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.4% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.006. Suppose the test is given to seven randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all seven people? (b) What is the probability that the test comes back positive for at least one of the seven people?

A new medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.74. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 14 % of the population who take this test have the disease.If the test administered to an individual is positive, what is the probability that the person actually has the disease?

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? ​(b) What is the probability that the test comes back positive for at least one of the six ​people?

Assume that among the general population, 13 people out of every 1000 have HIV/AIDS.  A pharmaceutical company designs a screening test for HIV/AIDS that has a 99% sensitivity and an 89% specificity.  Given that someone has a positive test result, what is the probability they have HIV/AIDS?