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(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...") |
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He carries out a test that will be positive with probability .8 if the patient | 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 | 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 | the outcome of the test was positive, what probabilities should the doctor now assign to <math>d_1</math>? | ||
assign to | |||
'''References''' | '''References''' | ||
{{cite web |url=https://math.dartmouth.edu/~prob/prob/prob.pdf |title=Grinstead and Snell’s Introduction to Probability |last=Doyle |first=Peter G.|date=2006 |access-date=June 6, 2024}} | {{cite web |url=https://math.dartmouth.edu/~prob/prob/prob.pdf |title=Grinstead and Snell’s Introduction to Probability |last=Doyle |first=Peter G.|date=2006 |access-date=June 6, 2024}} | ||
Revision as of 22:23, 22 June 2024
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]?
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.