A person must pay $10 to play a certain game at the casino. Each player has a probability of 0.03 of winning $ 13. What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places. Expected Value - $ -9.31 If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind? ahead behind Question Help: Message instructor Add Work Submit Question

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**Casino Game Expected Value Calculation**

**Problem Statement:**

A person must pay $10 to play a certain game at the casino. Each player has a probability of 0.03 of winning $13.

**Question:**

What is the Expected Value for the player (that is, the mean of the probability distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places.

**Calculation:**

- Expected Value (E) is calculated using the formula:

  \[
  E = ( \text{Probability of Winning} \times \text{Winnings} ) + ( \text{Probability of Losing} \times \text{Loss} )
  \]

- Given:
  - Probability of Winning = 0.03
  - Winnings = $13
  - Probability of Losing = 1 - 0.03 = 0.97
  - Cost to Play (Loss) = -$10

Substitute these into the formula:

  \[
  E = (0.03 \times 13) + (0.97 \times -10) = 0.39 - 9.7 = -9.31
  \]

  The Expected Value is **-9.31**.

**Answer Validation:**

- The provided answer is marked incorrect with a red 'X'.

**Follow-up Question:**

If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind?

- Options:
  - ☐ ahead
  - ☑ behind

  Selected answer: behind, marked correct with a green check.

**Additional Resources:**

- Question Help:
  - Message instructor
  - Add Work

---
Transcribed Image Text:--- **Casino Game Expected Value Calculation** **Problem Statement:** A person must pay $10 to play a certain game at the casino. Each player has a probability of 0.03 of winning $13. **Question:** What is the Expected Value for the player (that is, the mean of the probability distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places. **Calculation:** - Expected Value (E) is calculated using the formula: \[ E = ( \text{Probability of Winning} \times \text{Winnings} ) + ( \text{Probability of Losing} \times \text{Loss} ) \] - Given: - Probability of Winning = 0.03 - Winnings = $13 - Probability of Losing = 1 - 0.03 = 0.97 - Cost to Play (Loss) = -$10 Substitute these into the formula: \[ E = (0.03 \times 13) + (0.97 \times -10) = 0.39 - 9.7 = -9.31 \] The Expected Value is **-9.31**. **Answer Validation:** - The provided answer is marked incorrect with a red 'X'. **Follow-up Question:** If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind? - Options: - ☐ ahead - ☑ behind Selected answer: behind, marked correct with a green check. **Additional Resources:** - Question Help: - Message instructor - Add Work ---
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