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\begin{align*} P\left(A_{G} \cup A_{R}\right)=P\left(A_{G}\right)+P\left(A_{R}\right)-P\left(A_{G}-A_{R}\right)=\frac{6}{36}+\frac{6}{36}-\frac{1}{36}=\frac{11}{36} \end{align*}