For devotees of Star Trek a question of fundamental interest is whether the fatality rates and uniform color are independent. The table below summarizes the fatality and survivor counts in one of the Star Trek episodes.$$ \begin{array}{l|ccc|} & \text{Blue} & \text{Gold} & \text{Red}\\ \hline \text{Dead} & 7 & 9 & 24\\ \text{Alive} & 129 & 46 & 215\\ \hline \end{array} $$Use $\chi^2$ test for independence to test the hypothesis that fatality rates and uniform color are independent at the $5\%$ level of significance. Make sure to report $p$-value and draw a conclusion in the context of the problem.