Originally Posted by **mika**

There are two diagnostic tests for a disease. Among those who have the disease, 10% give negative results for the first test and, independently of this, 5% give negative results on the second test. Among those who do not have the disease, 80% give negative results on the first test and, independently, 70% give negative results on the second test. From historical data it is known that 20% of those sent by their GPs for diagnostic testing actually have the disease.

a) If both tests are negative, what is the probability that the person tested has the disease?