A doctor assumes that a patient has one of three diseases [math]d_1[/math], [math]d_2[/math], or [math]d_3[/math]. Before any test, he assumes an equal probability for each disease. He carries out a test that will be positive with probability .8 if the patient has [math]d_1[/math], .6 if he has disease [math]d_2[/math], and .4 if he has disease [math]d_3[/math]. Given that the outcome of the test was positive, what probabilities should the doctor now assign to the three possible diseases?