P = \frac{1}{6 \cdot 2^6} \sum_{k=1}^{6} \binom{6}{k} = \frac{1}{384} \left( \sum_{k=0}^{6} \binom{6}{k} - \binom{6}{0} \right) = \frac{1}{384} (2^6 - 1) = \frac{63}{384}.