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?

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?