Answer :
Certainly! Let's carefully consider each option in light of the given expected value of -[tex]$5.00 for the game.
1. Expected Value Concept:
- The expected value of a game indicates the average result you would get per play if you played the game a large number of times. An expected value of -$[/tex]5.00 means that, on average, you would lose [tex]$5.00 per play over a long period.
2. Analyzing Each Option:
- Option A: "Every time you play the game, you will lose $[/tex]5.00."
- This statement is incorrect because the expected value is an average, not a guarantee for each individual play. Some plays might have different outcomes, such as winning or losing different amounts.
- Option B: "If you played the game a large number of times, you'd lose an average of about [tex]$5.00 per play."
- This statement is correct. The expected value of -$[/tex]5.00 indicates that over many plays, your average loss would be [tex]$5.00 per play. This describes the long-term outcome that you would expect when playing the game repeatedly.
- Option C: "If you play the game five times, you are guaranteed to lose money."
- This statement is not necessarily true. While there's a high chance of losing money given the negative expected value, games of chance can have variability, and it's possible (though unlikely) to come out ahead or break even in a few plays.
- Option D: "You will gain an average of $[/tex]5.00 each time you play the game."
- This statement is incorrect as it contradicts the given expected value. With an expected value of -[tex]$5.00, you would expect to lose, not gain.
3. Conclusion:
- The correct interpretation is provided in Option B. If you played the game a large number of times, you would lose an average of about $[/tex]5.00 per play. This aligns with the concept of expected value, which averages out to that amount over many repetitions of the game.
1. Expected Value Concept:
- The expected value of a game indicates the average result you would get per play if you played the game a large number of times. An expected value of -$[/tex]5.00 means that, on average, you would lose [tex]$5.00 per play over a long period.
2. Analyzing Each Option:
- Option A: "Every time you play the game, you will lose $[/tex]5.00."
- This statement is incorrect because the expected value is an average, not a guarantee for each individual play. Some plays might have different outcomes, such as winning or losing different amounts.
- Option B: "If you played the game a large number of times, you'd lose an average of about [tex]$5.00 per play."
- This statement is correct. The expected value of -$[/tex]5.00 indicates that over many plays, your average loss would be [tex]$5.00 per play. This describes the long-term outcome that you would expect when playing the game repeatedly.
- Option C: "If you play the game five times, you are guaranteed to lose money."
- This statement is not necessarily true. While there's a high chance of losing money given the negative expected value, games of chance can have variability, and it's possible (though unlikely) to come out ahead or break even in a few plays.
- Option D: "You will gain an average of $[/tex]5.00 each time you play the game."
- This statement is incorrect as it contradicts the given expected value. With an expected value of -[tex]$5.00, you would expect to lose, not gain.
3. Conclusion:
- The correct interpretation is provided in Option B. If you played the game a large number of times, you would lose an average of about $[/tex]5.00 per play. This aligns with the concept of expected value, which averages out to that amount over many repetitions of the game.
