Take 10000 people, 2000 will have the disease (20 percent) and 8000 won't have the disease.
of the 2000 that have the disease, 1400 test positive (.7*2000)
of the 8000 that do not have the disease, (8000*.1) 800 will test postive
so a total of 800+1400=2200 will test postive.
but 2000 have the disease, so the probability of testing positive and having the disease is 2000/2200=.91 about.
A new medical test has been designed to detect the presence of the mysterious Brainlesserian disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.7. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.1. It is estimated that 20 % 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?
1 answer