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Question 5 (Multiple Choice, Worth 2 points)
In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 10 is [tex]\frac{3}{36}[/tex]. Predict how many times the rolls will result in a sum greater than 10 if the experiment is repeated 108 times.
Certainly! Let's work through predicting how many times the dice rolls will result in a sum greater than 10 if the experiment is repeated 108 times, using the given theoretical probability.
### Step-by-Step Solution:
1. Identify the Theoretical Probability: - The theoretical probability that the sum of two dice rolls will be greater than 10 is given as [tex]\(\frac{3}{36}\)[/tex].
2. Convert the Fraction to Decimal (to Understand the Probability Better): - [tex]\(\frac{3}{36} = 0.0833...\)[/tex] - So, the probability is approximately 0.0833 (or 8.33%).
3. Determine the Number of Trials: - The number of times the experiment is repeated is 108.
4. Calculate the Expected Number of Successful Outcomes: - Multiply the total number of trials by the probability of the successful outcome. - Expected outcomes [tex]\(= 0.0833 \times 108 \approx 9\)[/tex]
5. Conclusion: - It's predicted that the rolls will result in a sum greater than 10 approximately 9 times if the experiment is repeated 108 times.
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