Your School's Soccer Team Plays Two Games Against Another Soccer $$\begin{array} { l | c c c } \text { Games won } & 0 & 1 & 2 \\\hline \mathrm { P } \text { (Games won) } & 0.12 & 0.46 & 0.42\end{array}$$

Your school's soccer team plays two games against another soccer team.The probability that your team wins the first game is 0.6.If your team wins the first game,the probability that they also win the second game is 0.7.If your team loses the first game,the probability that they win the second game is 0.5.Let the random variable X be the number of games won by your team.Find the probability model for X.

A) $$\begin{array} { l | c c c } \text { Games won } & 0 & 1 & 2 \\\hline \mathrm { P } \text { (Games won) } & 0.12 & 0.46 & 0.42\end{array}$$
B) $$\begin{array} { l | l c c } \text { Games won } & 0 & 1 & 2 \\\hline \mathrm { P } \text { (Games won) } & 0.2 & 0.2 & 0.42\end{array}$$
C) $$\begin{array} { l | l c c } \text { Games won } & 0 & 1 & 2 \\\hline \text { P(Games won) } & 0.2 & 0.5 & 0.3\end{array}$$
D) $$\begin{array} { l | l c c } \text { Games won } & 0 & 1 & 2 \\\hline \text { P(Games won) } & 0.2 & 0.18 & 0.42\end{array}$$
E) $$\begin{array} { l | l c c } \text { Games won } & 0 & 1 & 2 \\\hline \text { P(Games won) } & 0.2 & 0.38 & 0.42\end{array}$$