The expected value of a game involving rolling two dice and taking the positive dif...
Check the final answer first, then review the worked steps.
Answer
C
Step-by-step solution
- Understand the Game: The game involves rolling a 7-sided die and a 5-sided die. The points awarded in a turn are the positive difference between the numbers rolled. Let $X$ be the random variable representing the points in a given turn.
- Analyze Yazmin's Statement: Yazmin states that the average number of points per turn will be about $2.14$. This directly refers to the expected value of $X$, denoted as $E(X)$. The problem statement itself provides that $E(X) \approx 2.14$ points. Therefore, Yazmin's statement is correct.
- Analyze Hannah's Statement: Hannah states that over $1,000$ turns, the total points can be expected to be about $214$. The expected total points over $N$ turns is $N \times E(X)$. In this case, $N = 1000$ and $E(X) \approx 2.14$. So, the expected total points are $1000 \times 2.14 = 2140$. Hannah's statement claims the total will be about $214$, which is significantly different from $2140$. Therefore, Hannah's statement is incorrect.
- Conclusion: Based on the analysis, only Yazmin's statement is correct.