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Baye's Theorem - Solved Problem

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A mail order company employs three stock clerks, A,B and C, who pull items from shelves and assemble them for subsequent verification and packaging. A makes a mistake in an order (gets an item wrong or the wrong quantity) one time in a hundred, B makes a mistake in an order five times in a hundred and C makes a mistake in an order three times in a hundred. If A, B and C fill respectively 30, 40 and 30 percent of all orders, what are the probabilities that

a) a mistake will be made in an order;
b) if a mistake is made in an order, it was filled by A;
c) if a mistake is made in an order, it was filled by B?

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The problem based on Baye's Theorem is solved step by step and explanation is given in such a way that the student can use this solution as a model to solve other problems of the same type.

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1. A bag contains 10 red, 12 green, and 8 yellow marbles. Assuming that all marbles are equally likely to be picked from the bag, what is the probability that the second marble is yellow, given that the first marble was yellow?

2. Given the following information, calculate the Predictive value positive and the Predictive value negative.

Prevalence =5%
Sensitivity =85%
Specificity =74%

3. Find a steady state distribution vector for the Markov chain with transition

[0.25 0.75]
P=
[0.2 0.8]

4. A couple has 8 foster children, including 3 girls and 5 boys. Two-thirds of the girls have brown eyes. What is the probabiliy that a randomly selected child is a brown-eyed girl?

5. The probability of moving from a state i to a state j is called the?

6. Given the following information, compute the PVP using Bayes' Theorem. Prevalence = 20% Sensitivity = 50% Specificity = 75%

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