Question
In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 10 is 3 over 36. Predict how many times the rolls will result in a sum greater than 10 if the experiment is repeated 108 times.
3
9
10
18
3
9
10
18
Answers
GPT-4o mini
To solve this problem, we need to determine how many times the rolls will result in a sum greater than 10 if the experiment is repeated 108 times.
We know that the theoretical probability of rolling a sum greater than 10 is given as \(\frac{3}{36}\). This can be simplified to \(\frac{1}{12}\).
To predict the number of times we expect to get a sum greater than 10 in 108 trials, we multiply the probability by the number of trials:
\[
\text{Expected number of successes} = \text{Probability} \times \text{Number of trials}
\]
\[
= \frac{1}{12} \times 108
\]
Calculating this gives:
\[
= \frac{108}{12} = 9
\]
Therefore, if the experiment is repeated 108 times, we expect the rolls will result in a sum greater than 10 approximately **9 times**.
The correct answer is **9**.
We know that the theoretical probability of rolling a sum greater than 10 is given as \(\frac{3}{36}\). This can be simplified to \(\frac{1}{12}\).
To predict the number of times we expect to get a sum greater than 10 in 108 trials, we multiply the probability by the number of trials:
\[
\text{Expected number of successes} = \text{Probability} \times \text{Number of trials}
\]
\[
= \frac{1}{12} \times 108
\]
Calculating this gives:
\[
= \frac{108}{12} = 9
\]
Therefore, if the experiment is repeated 108 times, we expect the rolls will result in a sum greater than 10 approximately **9 times**.
The correct answer is **9**.