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SusanAthena, Master's Degree
Category: Calculus and Above
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# An urn contains 6 red. At each round we pick a random ball

### Customer Question

An urn contains 6 red balls. At each round we pick a random ball from the urn and replace it with a blue ball. The experiment ends when there are no more red balls in urn. What the is the expectation on number of rounds needed to complete the experiment?
Question 1. A strategy determines who shoots at whom at every round. Determine the best strategy for all three players. Explain why.
Question 2. Create a Markov Chain to solve this problem.
(a) First list all states.
(b) Second make a connections and determine the probabilities.
(c) Create a Markov diagram (graph).
(d) Determine all absorbing states.
(e) Create transition Matrix.
(f) Compute the winning probabilities for all players as well as probability that no one would survive.
(g) What is the expectation on number of rounds needed to finish the truel? Hint: Recall that for absorbing cases the k-th power of the matrix represents the probability of getting into the absorbing case UP TO k-th round.
Submitted: 7 months ago.
Category: Calculus and Above
Customer: replied 7 months ago.
I have tried to attempt this problem, but do not know where to start.
Expert:  George Sibiya replied 7 months ago.

Hi,

Welcome to JustAnswer. How soon do you need it completed?

Regards,

George

Customer: replied 7 months ago.
By tomorrow would be great. Thank you for your help
Expert:  George Sibiya replied 7 months ago.

Ok cool. I will update you on the progress.

Customer: replied 7 months ago.
Just looked over what I posted earlier and noticed I added the Question 1 and 2. Please disregard question 1 and 2. I only need help with the very first part about the urn and balls. Thank you.