A test for a certain rare disease is assumed to be correct 100x% of the time. That is, if a person has the disease, the test results are positive with probability x, and if the person does not have the disease, the test results are negative with probability x. A random person drawn from a certain population has probability 0.001 of having the disease.

(a) Given that the person just tested positive, what is the probability of the person having the disease? (Find an expression for this probability in terms of x)

(b) Let p(x) be the probability in (a). Plot p(x) against x, and find the minimum accuracy x of the test such that p(x) is at least 0.99.