Solve using a decision tree:Dr Frank N. Stine, a physician at the Transylvania Health Centre, is visited by a student, Elizabeth Gore. E.Gore is suffering from one of two illnesses x or y. The physician can either diagnose immediately or perform a test which will give him additional information. Suppose the prior probability of disease x is 0,8 and disease y is 0,2. The physician also has the following information on the test, which gives either a positive or negative result:

p(positive result | x) = 0,9

p(positive result | y) = 0,2

If the value of a correct diagnosis without the test is 100, with the test 80 and a mis-diagnosis is zero regardless of whether the test is performed, should the physician diagnose with or without the test?