4.146 A screening test for a certain disease is prone to giving false positives or false negatives. If a patient being tested has the disease, the probability that the test indicates a (false) negative is .13. If the patient does not have the disease, the probability that the test indicates a (false) positive is .10. Assume that 3% of the patients being tested actually have the disease. Suppose that one patient is chosen at random and tested. Find the probability that

a. this patient has the disease and tests positive

b. this patient does not have the disease and tests positive

c. this patient tests positive

d. this patient has the disease given that he or she tests positive

(Hint: A tree diagram may be helpful in part c.)