Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Tanya is considering playing a game at the fair. There are three different games to choose from, and it costs \[tex]$2 to play a game. The probabilities associated with the games are given in the table.

\[
\begin{tabular}{|l|c|c|c|}
\hline
& Lose \$[/tex]2 & Win \[tex]$1 & Win \$[/tex]4 \\
\hline
Game 1 & 0.55 & 0.20 & 0.25 \\
\hline
Game 2 & 0.15 & 0.35 & 0.50 \\
\hline
Game 3 & 0.20 & 0.60 & 0.20 \\
\hline
\end{tabular}
\]

a. What is the expected value for playing each game?

b. If Tanya decides she will play the game, which game should she choose? Explain.

Sagot :

GinnyAnswer
Let's solve this problem step-by-step.

### Part a: Expected Value Calculation

The expected value for each game can be calculated using the formula:
[tex]\[ \text{Expected Value} = \sum (\text{Payout} \times \text{Probability}) \][/tex]

#### Game 1:
- Lose \[tex]$2 with probability 0.55 - Win \$[/tex]1 with probability 0.20
- Win \[tex]$4 with probability 0.25 Calculate the expected value: \[ \text{Expected Value for Game 1} = (-2 \times 0.55) + (1 \times 0.20) + (4 \times 0.25) \] \[ = -1.1 + 0.2 + 1.0 \] \[ = 0.10 \] #### Game 2: - Lose \$[/tex]2 with probability 0.15
- Win \[tex]$1 with probability 0.35 - Win \$[/tex]4 with probability 0.50

Calculate the expected value:
[tex]\[ \text{Expected Value for Game 2} = (-2 \times 0.15) + (1 \times 0.35) + (4 \times 0.50) \][/tex]
[tex]\[ = -0.3 + 0.35 + 2.0 \][/tex]
[tex]\[ = 2.05 \][/tex]

#### Game 3:
- Lose \[tex]$2 with probability 0.20 - Win \$[/tex]1 with probability 0.60
- Win \[tex]$4 with probability 0.20 Calculate the expected value: \[ \text{Expected Value for Game 3} = (-2 \times 0.20) + (1 \times 0.60) + (4 \times 0.20) \] \[ = -0.4 + 0.6 + 0.8 \] \[ = 1.00 \] ### Summary of Expected Values - Expected Value for Game 1: \$[/tex]0.10
- Expected Value for Game 2: \[tex]$2.05 - Expected Value for Game 3: \$[/tex]1.00

### Part b: Which Game Should Tanya Choose?

The expected value represents the average amount she expects to win per game in the long run. Among the three games, we compare the expected values:

- Game 1: \[tex]$0.10 - Game 2: \$[/tex]2.05
- Game 3: \[tex]$1.00 Since Game 2 has the highest expected value of \$[/tex]2.05, Tanya should choose Game 2 to maximize her expected winnings.
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.