# Problems: Probability, Markov Chain, Baye's Theorem

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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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