In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 9 is 6 over 36. Predict how many times the rolls will result in a sum greater than 9 if the experiment is repeated 144 times.

 24
 12
 9
 6

To solve this problem, we need to apply the theoretical probability and scale it to the number of trials (144 experiments).

1. **Given Probability**:
   The theoretical probability of getting a sum greater than 9 when rolling two dice is \( \frac{6}{36} \) (since there are 6 favorable outcomes and 36 total possible outcomes).

2. **Simplify the Probability**:
   \( \frac{6}{36} = \frac{1}{6} \).

3. **Number of Trials**:
   The experiment is repeated 144 times.

4. **Expected Number of Successes**:
   To predict how many times the sum will be greater than 9, multiply the probability by the number of trials:
   \[
   \text{Expected Successes} = \frac{1}{6} \times 144 = 24.
   \]

So, the correct prediction is **24**.

Let me know if you'd like more details or have any questions!

Here are 5 related questions for further exploration:
1. What is the probability of rolling a sum of exactly 9?
2. How many outcomes give a sum less than 5?
3. What is the expected number of sums less than or equal to 7 if the experiment is repeated 100 times?
4. What are all possible outcomes when rolling two dice?
5. How does the probability change if the dice are biased?

**Tip**: When calculating probabilities for repeated experiments, multiplying the probability of a single event by the number of trials is a key step.

In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 9 is 6 over 36. Predict how many times the rolls will result in a sum greater than 9 if the experiment is repeated 144 times.

Learn how to predict the number of times the sum of two dice rolls will be greater than 9, using theoretical probability. This problem involves calculating expected value, and scaling probability over 144 trials. Suitable for students in Grades 6-8.

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