\begin{pmatrix} P_A(i) \\ P_B(i) \\ \end{pmatrix} = \begin{pmatrix}\frac{4}{5} - \frac{4 \left(- \frac{1}{4}\right)^{i}}{5}\\\frac{4 \left(- \frac{1}{4}\right)^{i}}{5} + \frac{1}{5}\end{pmatrix}
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