exercise:9216b4c64a: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> 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...") |
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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. | |||
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 | 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 the three possible diseases? | assign to the three possible diseases? | ||
Latest revision as of 23:45, 12 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 the three possible diseases?