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In this question you will find the steady-state probability distribution for the regular transition matrix below with 3 states A, B, and C. A B

In this question you will find the steady-state probability distribution for the regular transition matrix below with 3 states A, B, and C.

A B C

A 0.0 0.5 0.5
B 0.2 0.4 0.4
C 0.3 0.4 0.3

Give the following answers as fractions OR as decimals correct to at least 5 decimal places.

What is the long term probability of being in state A? What is the long term probability of being in state B? What is the long term probability of being in state C?

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