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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.

A. 3
B. 9
C. 10
D. 18

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Question 6 (Multiple Choice, Worth 2 points)



Answer :

GinnyAnswer
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.

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