4 A game has a 10 dollar buy in. You have 20% to win nothing, 20% to win 5 dollars, 30% to break even, and 30% to win 20 dollars. What is the games

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The text in the image poses a probability question related to expected value (EV):

"A game has a 10 dollar buy-in. You have 20% to win nothing, 20% to win 5 dollars, 30% to break even, and 30% to win 20 dollars. What is the game's EV?"

To calculate the expected value, we need to consider the probability and outcome of each event:

- 20% chance to win nothing: \$0
- 20% chance to win 5 dollars: \$5
- 30% chance to break even: \$10
- 30% chance to win 20 dollars: \$20

Calculate the expected value (EV) using the formula:

EV = (Probability of Outcome 1) * (Outcome 1) + (Probability of Outcome 2) * (Outcome 2) + ...

Here is the breakdown:

EV = (0.20 * \$0) + (0.20 * \$5) + (0.30 * \$10) + (0.30 * \$20)

Explain each calculation:
1. The chance of winning nothing results in zero return.
2. The chance of winning $5 contributes to part of the expected winnings.
3. The chance of breaking even simply returns the initial buy-in.
4. The chance of winning $20 significantly affects the expected value.

Substitute the calculations and solve for the EV to determine the financial expectation of playing the game.

This represents a basic approach to understanding probability and how expected value is used in decision making in potential gamble-like scenarios.
Transcribed Image Text:The text in the image poses a probability question related to expected value (EV): "A game has a 10 dollar buy-in. You have 20% to win nothing, 20% to win 5 dollars, 30% to break even, and 30% to win 20 dollars. What is the game's EV?" To calculate the expected value, we need to consider the probability and outcome of each event: - 20% chance to win nothing: \$0 - 20% chance to win 5 dollars: \$5 - 30% chance to break even: \$10 - 30% chance to win 20 dollars: \$20 Calculate the expected value (EV) using the formula: EV = (Probability of Outcome 1) * (Outcome 1) + (Probability of Outcome 2) * (Outcome 2) + ... Here is the breakdown: EV = (0.20 * \$0) + (0.20 * \$5) + (0.30 * \$10) + (0.30 * \$20) Explain each calculation: 1. The chance of winning nothing results in zero return. 2. The chance of winning $5 contributes to part of the expected winnings. 3. The chance of breaking even simply returns the initial buy-in. 4. The chance of winning $20 significantly affects the expected value. Substitute the calculations and solve for the EV to determine the financial expectation of playing the game. This represents a basic approach to understanding probability and how expected value is used in decision making in potential gamble-like scenarios.
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