Consider the dreaded disease Dipsidoodleitis. There are actually two forms of the disease, Type I and Type II, with the latter being more severe. Dipsidoodleitis is detected by a blood test. Values for people without dipsidoodleitis are normally distributed, M=70, sd=10. Values for people with Type I and Type II are distributed with M=80, sd=14, and M=110, sd=20, respectively. If a patient has a value of 90, what are the probabilities that she is dipsidoodleitis free, has the Type I version, or has the Type II version

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Please use  Bayes' Theorem and show the prior, posterior, and the prior and posterior solution. 

Consider the dreaded disease Dipsidoodleitis. There are actually two forms of the disease, Type I and Type II, with the latter being more severe. Dipsidoodleitis is detected by a blood test. Values for people without dipsidoodleitis are normally distributed, M=70, sd=10. Values for people with Type I and Type II are distributed with M=80, sd=14, and M=110, sd=20, respectively. If a patient has a value of 90, what are the probabilities that she is dipsidoodleitis free, has the Type I version, or has the Type II version

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