\begin{pmatrix} P_A(i) \\ P_B(i) \\ \end{pmatrix} = \begin{pmatrix} 3/4 & 1 \\ 1/4 & 0 \\ \end{pmatrix} ^i \begin{pmatrix} P_A(0) \\ P_B(0) \\ \end{pmatrix}
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