A carnival game offers a(n)$80 cash prize for anyone who can break a balloon by throwing a dart at it.It costs $5 to play and you're willing to spend up to $20 trying to win.You estimate that you have a(n)12% chance of hitting the balloon on any throw. Create a probability model for the amount you will win.Assume that throws are independent of each other.Round to four decimal places if necessary.
A) $$\begin{array} { l | l c c c c }
\text { Amount won } & \$ 75 & \$ 70 & \$ 65 & \$ 60 & - \$ 20 \
\hline \mathrm { P } \text { (Amount won } ) & 0.12 & 0.1056 & 0.0929 & 0.0818 & 0.0720
\end{array}$$
B) $$\begin{array} { l | l c c c }
\text { Amount won } & \$ 75 & \$ 70 & \$ 65 & \$ 60 \
\hline \mathrm { P } \text { (Amount won) } & 0.12 & 0.1056 & 0.0929 & 0.6815
\end{array}$$
C) $$\begin{array} { l | l c c c c }
\text { Amount won } & \$ 80 & \$ 75 & \$ 70 & \$ 65 & - \$ 20 \
\hline \mathrm { P } \text { (Amount won } ) & 0.12 & 0.1056 & 0.0929 & 0.0818 & 0.0720
\end{array}$$
D) $$\begin{array} { l | l c c c c }
\text { Amount won } & \$ 75 & \$ 70 & \$ 65 & \$ 60 & - \$ 20 \
\hline \mathrm { P } \text { (Amount won } ) & 0.12 & 0.1056 & 0.0929 & 0.0818 & 0.5997
\end{array}$$
E) $$\begin{array} { l | l c c c c }
\text { Amount won } & \$ 80 & \$ 75 & \$ 70 & \$ 65 & - \$ 20 \
\hline \mathrm { P } \text { (Amount won } ) & 0.12 & 0.1056 & 0.0929 & 0.0818 & 0.5997
\end{array}$$

Question

A carnival game offers a(n)$80 cash prize for anyone who can break a balloon by throwing a dart at it.It costs $5 to play and you're willing to spend up to $20 trying to win.You estimate that you have a(n)12% chance of hitting the balloon on any throw. Create a probability model for the amount you will win.Assume that throws are independent of each other.Round to four decimal places if necessary.
A) $$\begin{array} { l | l c c c c } 
\text { Amount won } & \$ 75 & \$ 70 & \$ 65 & \$ 60 & - \$ 20 \
\hline \mathrm { P } \text { (Amount won } ) & 0.12 & 0.1056 & 0.0929 & 0.0818 & 0.0720
\end{array}$$
B) $$\begin{array} { l | l c c c } 
\text { Amount won } & \$ 75 & \$ 70 & \$ 65 & \$ 60 \
\hline \mathrm { P } \text { (Amount won) } & 0.12 & 0.1056 & 0.0929 & 0.6815
\end{array}$$
C) $$\begin{array} { l | l c c c c } 
\text { Amount won } & \$ 80 & \$ 75 & \$ 70 & \$ 65 & - \$ 20 \
\hline \mathrm { P } \text { (Amount won } ) & 0.12 & 0.1056 & 0.0929 & 0.0818 & 0.0720
\end{array}$$
D) $$\begin{array} { l | l c c c c } 
\text { Amount won } & \$ 75 & \$ 70 & \$ 65 & \$ 60 & - \$ 20 \
\hline \mathrm { P } \text { (Amount won } ) & 0.12 & 0.1056 & 0.0929 & 0.0818 & 0.5997
\end{array}$$
E) $$\begin{array} { l | l c c c c } 
\text { Amount won } & \$ 80 & \$ 75 & \$ 70 & \$ 65 & - \$ 20 \
\hline \mathrm { P } \text { (Amount won } ) & 0.12 & 0.1056 & 0.0929 & 0.0818 & 0.5997
\end{array}$$

Quizplus · Accepted Answer

Let X be the amount you will win. 
The possible outcomes for X are: 
- You win $75 with probability 0.12, since you can win $80 but you spent $5 to play. 
- You lose $5 with probability 0.88, since you don't win anything but you spent $5 to play.

Therefore, the probability model for X is:

|   X   |  75  | -5   |
|-------|------|------|
| P(X)  | 0.12 | 0.88 |

To find the expected value of X, we multiply each outcome by its probability and sum the results:

E(X) = ($75)(0.12) + (-$5)(0.88) = -$3.4

Since the expected value of X is negative, it means that on average you will lose money by playing this game. Therefore, it's not a good choice to spend up to $20 trying to win.

A Carnival Game Offers A(n)$80 Cash Prize for Anyone Who