\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A pair of colored dice (one red and one blue) is rolled. Each die has faces numbered 1 to 6. The table below shows the possible outcomes for the two dice.
\(\begin{aligned} & \textcolor{colorprop}{\text{blue die}} \\ \textcolor{colordef}{\text{red die}} \end{aligned} \) \(\textcolor{colorprop}{1}\) \(\textcolor{colorprop}{2}\) \(\textcolor{colorprop}{3}\) \(\textcolor{colorprop}{4}\) \(\textcolor{colorprop}{5}\) \(\textcolor{colorprop}{6}\)
\(\textcolor{colordef}{1}\) \(\textcolor{colordef}{1}\textcolor{colorprop}{1}\) \(\textcolor{colordef}{1}\textcolor{colorprop}{2}\) \(\textcolor{colordef}{1}\textcolor{colorprop}{3}\) \(\textcolor{colordef}{1}\textcolor{colorprop}{4}\) \(\textcolor{colordef}{1}\textcolor{colorprop}{5}\) \(\textcolor{colordef}{1}\textcolor{colorprop}{6}\)
\(\textcolor{colordef}{2}\) \(\textcolor{colordef}{2}\textcolor{colorprop}{1}\) \(\textcolor{colordef}{2}\textcolor{colorprop}{2}\) \(\textcolor{colordef}{2}\textcolor{colorprop}{3}\) \(\textcolor{colordef}{2}\textcolor{colorprop}{4}\) \(\textcolor{colordef}{2}\textcolor{colorprop}{5}\) \(\textcolor{colordef}{2}\textcolor{colorprop}{6}\)
\(\textcolor{colordef}{3}\) \(\textcolor{colordef}{3}\textcolor{colorprop}{1}\) \(\textcolor{colordef}{3}\textcolor{colorprop}{2}\) \(\textcolor{colordef}{3}\textcolor{colorprop}{3}\) \(\textcolor{colordef}{3}\textcolor{colorprop}{4}\) \(\textcolor{colordef}{3}\textcolor{colorprop}{5}\) \(\textcolor{colordef}{3}\textcolor{colorprop}{6}\)
\(\textcolor{colordef}{4}\) \(\textcolor{colordef}{4}\textcolor{colorprop}{1}\) \(\textcolor{colordef}{4}\textcolor{colorprop}{2}\) \(\textcolor{colordef}{4}\textcolor{colorprop}{3}\) \(\textcolor{colordef}{4}\textcolor{colorprop}{4}\) \(\textcolor{colordef}{4}\textcolor{colorprop}{5}\) \(\textcolor{colordef}{4}\textcolor{colorprop}{6}\)
\(\textcolor{colordef}{5}\) \(\textcolor{colordef}{5}\textcolor{colorprop}{1}\) \(\textcolor{colordef}{5}\textcolor{colorprop}{2}\) \(\textcolor{colordef}{5}\textcolor{colorprop}{3}\) \(\textcolor{colordef}{5}\textcolor{colorprop}{4}\) \(\textcolor{colordef}{5}\textcolor{colorprop}{5}\) \(\textcolor{colordef}{5}\textcolor{colorprop}{6}\)
\(\textcolor{colordef}{6}\) \(\textcolor{colordef}{6}\textcolor{colorprop}{1}\) \(\textcolor{colordef}{6}\textcolor{colorprop}{2}\) \(\textcolor{colordef}{6}\textcolor{colorprop}{3}\) \(\textcolor{colordef}{6}\textcolor{colorprop}{4}\) \(\textcolor{colordef}{6}\textcolor{colorprop}{5}\) \(\textcolor{colordef}{6}\textcolor{colorprop}{6}\)
Calculate the probability that the sum of the two dice is exactly 7, simplifying the fraction.
\(P(\text{"sum is 7"}) =\)