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 [math]d_1[/math]?

• 4/9
• 1/2
• 2/3
• 3/5
• 4/5

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.