In a certain population, 1% of all individuals are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for non-carriers that the diagnostic test is applied independently to two different samples from the same randomly selected individual.   What is the probability that both tests yield the same results?

It is estimated that 1% of the population has a certain genetic defect. A medical test is used to determine if people have this defect and, if a person has this defect, the test will correctly indicate this with probability 90%. However, if a person does not have this defect, the test will still indicate that he or she has the defect with probability 9.6%. If a person tests positive for this defect, what is the probability that the person actually has the defect? Express your answer, rounded to three decimal places, if necessary.

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?

Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false positive in 4% of the cases where the disease is not present. What is the probability that the disease is absent if the test result is negative?

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 four randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all four people? (b) What is the probability that the test comes back positive for at least one of the four people? (a) P(all 4 tests are negative) = (Round to four decimal places as needed.) (b) P(at least one positive) = (Round to four decimal places as needed.)

3.7% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 90.2% of those who have the disease test positive. However, 3.9% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?

A drug test facility uses a test that has a 1% false negative rate, and a 2% false positive rate. It is estimated that 4% of the population is taking this drug. If a random person who tested positive is chosen, what is the probability that they are actually taking the drug?

A manufacturer wishes to estimate the accuracy of its final visual inspection process. A random sample of 180 devices is selected from production. An item is defective or “bad” if it contains at least one visually noticeable cosmetic defect.  The process improvement team agrees that the sample contains 27 bad items and 153 good items.  The team gives the items to a “certified” operator for inspection.  The operator rejects 10 good pieces and accepts 11 bad pieces and classifies the remainder correctly.  What is the probability that the inspector will reject an item?   P(inspector will reject an item) = ________%.  Enter value using one decimal place.