A screening test for a disease shows a positive test result in 95% of all cases when the disease is actually present and in 10% of all cases when it is not. If a result is positive, the test is repeated. Assume that the second test is independent of the first test. If the prevalence of the disease is 1 in 50 and an individual tests positive twice, compute the probability that the individual actually has the disease.

A drug test correctly gives a positive result 88 percent of the time. However, 3 percent of the time, it incorrectly gives a positive result. This is known as a false positive. Suppose that 5 percent of the people to be tested will have one or more of the drugs being tested for in their system. What is the probability that a randomly chosen person will have get a positive test result? Your answer should be to 4 decimal places.

Assume that n = 10, and p = 6/8. Find the probability of at least 1 success and at least 3 failures.

A certain disease has an incidence rate of 0.1%. If the false negative rate is 7% and the false positive rate is 3%, compute the probability that a person who tests positive actually has the disease.

The​ three-year recidivism rate of parolees in a certain state is about 20​%; that​ is, 20​% of parolees end up back in prison within three years. Assume that whether one parolee returns to prison is independent of whether any of the others return. Complete parts a and b below.         Find the probability that exactly 6 out of 20 parolees will end up back in prison within three years.   The probability that exactly 6 out of 20 parolees will end up back in prison is nothing.

In a video game, a specific attack succeeds at a rate of 20% and every try is independent. Determine the probability that the first attack lands on the 3rd try.

A certain disease has an incidence rate of 0.7%. If the false negative rate is 8% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.

Show all your work and explain each step. A laboratory blood test is 0.95 effective in detecting Corona virus, when it is, in fact, present. However, the test also yields a "false positive" result for 1 percent of the healthy persons tested. (That is, if a healthy person is tested, then, with probability 0.01, the result will imply s/he has the Corona virus.) If 0.5 percent of the population in King County has the virus, what is the probability a person has the virus given that his or her test result is positive?

A blood test indicates the presence of a particular disease 98​% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5​% of the time when the disease is not present. One percent of the population actually has the disease. Calculate the probability that a person has the​ disease, given that the test indicates the presence of the disease.

A certain disease has an incidence rate of 0.2%. If the false negative rate is 5% and the false positive rate is 1%, compute the probability that a person who tests positive actually has the disease.