Revision as of 20:42, 21 June 2024 by Admin (Created page with "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 thr...")
Jun 21'24
Exercise
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?
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.