Welcome to Bytelearn!

Let’s check out your problem:

part $2$: Carnival Games$\newline$$1$) ($7$ points) If you have been to a carnival or fair, you may remember a game where you throw a dart at a wall of balloons to pop them. Here is a similar game:$\newline$- There are $30$ balloons on the wall.$\newline$- $10$ of them contain prize tokens.$\newline$- The player pays $\$ 2$ and gets to throw darts until $2$ balloons pop. don't win anything.$\newline$Let's find the expected value for this game.$\newline$In order to fill in the table below, first complete the tree diagram, using fractions to label the probabilities on each branch and the final probabilities (w).$\newline$Now use the probabilities you found to fill in the table and compute the expected value of this game.$\newline$\begin{tabular}{|c|c|c|c|c|}$\newline$\hline \begin{tabular}{c} $\newline$Number of \\$\newline$tokens$\newline$\end{tabular} & \begin{tabular}{c} $\newline$Probability \\$\newline$(use fractions)$\newline$\end{tabular} & Payout & \begin{tabular}{c} $\newline$Value \\$\newline$(payout - \$\(2\) cost)\(\newline\)\end{tabular} & \begin{tabular}{c} \(\newline\)Weighted Value for the \\\(\newline\)player: \\\(\newline\)(use decimals, rounded to the \\\(\newline\)nearest penny)\(\newline\)\end{tabular} \\\(\newline\)\hline \(0\) & & \( \$ 0 \) & & \\\(\newline\)\hline \(1\) & & \( \$ 3 \) & & \\\(\newline\)\hline \(2\) & & \( \$ 4 \) & & \\\(\newline\)\hline \multicolumn{\(5\)}{|c|}{ Total Expected Value (Payout) for the player: } \\\(\newline\)\hline\(\newline\)\end{tabular}\(\newline\)Does the game favor the player or the game-runner? Explain.