SOLUTION: How do you apply the Bayes' Theorem? Thank you. Use Bayes Theorem for the following In the current second year class of a top ranked US university, all students come from t

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Question 974803: How do you apply the Bayes' Theorem? Thank you.
Use Bayes Theorem for the following
In the current second year class of a top ranked US university, all students come from three states in the US . Kansas, Illinois, and Ohio supply respectively 40%, 50%, and 10% of the students. The failure rate of students is 4%, 2%, and 6% respectively.
What is the probability that a student chosen at random will fail?
Given that a student fails , what is the probability that he or she came form Kansas?
Answer by solver91311(24713) About Me  (Show Source):
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Let denote the event that a randomly chosen student comes from state where and 1 represents Kansas, 2 represents Illinois, and 3 represents Ohio. Let represent the event that a randomly chosen student will fail. We are given the following infomation:



If a student is from Kansas, then the probability that student will fail is 0.04. That is to say: . By the same analysis, we have, overall:



To answer the first question, we use the following:



The arithmetic is left as an exercise for the student.

Second question: Given that has occurred, we then want to calculate the conditional probability of . By Bayes' Theorem:



The rest is arithmetic.

John

My calculator said it, I believe it, that settles it