There are two diagnostic tests for a disease. Among those who have the disease, 10% give negative results on 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. Twenty percent of those tested actually have the disease.

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

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

c) If the first test gives a positive result, what is the probability that the second test will also be positive?