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A marketing model tracks customers buying Brand A, Brand B, or Brand C. The transition matrix is:$$ \mathbf{T} = \begin{pmatrix} 0.8 & 0.1 & 0.1 \\ 0.1 & 0.7 & 0.2 \\ 0.1 & 0.2 & 0.7 \end{pmatrix} $$If a customer buys Brand B this week, what is the probability they will buy Brand C next week?
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