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 find out how many times we can predict that the rolls will result in a sum greater than 10 when the experiment is repeated 108 times, we can use the theoretical probability you've provided.
The theoretical probability of rolling a sum greater than 10 is \( \frac{3}{36} \). This can be simplified to \( \frac{1}{12} \).
Now, to find the expected number of times this event will occur in 108 experiments, we multiply the probability by the number of trials:
\[
\text{Expected occurrences} = \text{Probability} \times \text{Number of trials}
\]
\[
\text{Expected occurrences} = \frac{1}{12} \times 108
\]
Calculating that:
\[
\text{Expected occurrences} = \frac{108}{12} = 9
\]
Therefore, if Kim rolls the die 108 times, we predict that the rolls will result in a sum greater than 10 approximately **9 times**.
So the answer is **9**.
The theoretical probability of rolling a sum greater than 10 is \( \frac{3}{36} \). This can be simplified to \( \frac{1}{12} \).
Now, to find the expected number of times this event will occur in 108 experiments, we multiply the probability by the number of trials:
\[
\text{Expected occurrences} = \text{Probability} \times \text{Number of trials}
\]
\[
\text{Expected occurrences} = \frac{1}{12} \times 108
\]
Calculating that:
\[
\text{Expected occurrences} = \frac{108}{12} = 9
\]
Therefore, if Kim rolls the die 108 times, we predict that the rolls will result in a sum greater than 10 approximately **9 times**.
So the answer is **9**.