Newborn babies are routinely screened for a serious disease which affects only two per 1000 babies. The result of screening can be positive or negative. A positive result suggests that the baby. has the disease, but the test is not perfect. If a baby has the disease, the probability that the result will be negative is 0.01. If the baby does not have the disease, the probability that the result will be positive is 0.02.

(a) Find the probability that a baby has the disease, given that the result of the test is positive.

(b) Comment on the value you obtain. (L)