(Steps Shown) [9+2+2 = 13 pts] From a group of three Republicans, two Democrats, and one independent, a committee of two people is to be randomly selected.
Question: [9+2+2 = 13 pts]
From a group of three Republicans, two Democrats, and one independent, a committee of two people is to be randomly selected. Let Y 1 denote the number of Republicans and Y 2 denote the number of Democrats on the committee. Using the joint probability function p(y 1 , y 2 ), fill out the following table.
\[p({{y}_{1}},{{y}_{2}})=\frac{\left( \begin{aligned} & 3 \\ & {{y}_{1}} \\ \end{aligned} \right)\left( \begin{aligned} & 2 \\ & {{y}_{2}} \\ \end{aligned} \right)\left( \begin{aligned} & \text{ }1 \\ & 2-{{y}_{1}}-{{y}_{2}} \\ \end{aligned} \right)}{\left( \begin{aligned} & 6 \\ & 2 \\ \end{aligned} \right)}\] , y 1 = 0, 1, 2; y 2 = 0, 1, 2- What is \[{{p}_{1}}(2)?\]
- What is \[{{p}_{2}}(0)?\]
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