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An urn always contains two balls, where each ball is either red or blue. At each...

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Advance Math

An urn always contains two balls, where each ball is either red or blue.

At each stage a ball is randomly chosen from the urn. A drawn red
ball is always replaced with a blue ball. A drawn blue ball is equally
likely to be replaced by either a red or a blue ball. Suppose that the
urn initially has one red and one blue ball.
(a) Define a Markov chain that should be useful for the above model.
Define its states and give the transition probabilities.
(b) Find the probability that the second ball selected is red.
(c) Find the probability that the third ball selected is red.
(d) Find the long run proportion of time that both balls are red.
(e) Find the long run proportion of drawn balls that are red.

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