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.
So, the correct answer is:
- 9
This makes option 9 the correct choice.
