One bag contains red and green balls.
Kalyn randomly chooses one ball from the bag. Without replacement, he then chooses a second ball from the bag.
Complete the tree diagram below and then draw a probability distribution table for the number of red balls that could be drawn out of the bag. (3 marks)
--- 4 WORK AREA LINES (style=lined) ---
\begin{array}{|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt}& \quad 0 \quad & \quad 1 \quad & \quad 2 \quad \\
\hline
\rule{0pt}{2.5ex} P(X=x) \rule[-1ex]{0pt}{0pt}& \frac{5}{18} & \frac{5}{9} & \frac{1}{6} \\
\hline
\end{array}
`x = 2: \ P(R R) = 4/9 xx 3/8 = 1/6`
`x = 1: \ P(R and G) = 4/9 xx 5/8 + 5/9 xx 4/8 = 5/9`
`x = 0: \ P(G G) = 5/9 xx 4/8 = 5/18`
\begin{array}{|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt}& \quad 0 \quad & \quad 1 \quad & \quad 2 \quad \\
\hline
\rule{0pt}{2.5ex} P(X=x) \rule[-1ex]{0pt}{0pt}& \frac{5}{18} & \frac{5}{9} & \frac{1}{6} \\
\hline
\end{array}