For the given transistion matrix, find the probability that state 1 changes to state 2 after three repititions of the experiment.

C = [ .5 .5]

[ .72 .28]

What is the probability state 1 changes to state 2 after three repetitions of the experiment?

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To find the probability that state 1 changes to state 2 after 3 repetitions of the experiment, we look at the entry in row 1 column 2 of the cube of the transition matrix.

(In general, the `ij^(th)` entry of `P^m` , where `P^(m)` is the m-step transition matrix, is the probability of a transition from state `i` to state `j` .)

`P=([.5,.5],[.72,.28])`

`P^3=([.5858,.4142],[.5964,.4035])`

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The probability of changing from state 1 tio state 2 after 3 repetitions is approximately .4142

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