To determine the experimental probability of rolling two numbers that sum to 4, we'll go through the following steps:
1. Identify Possible Outcomes for a Sum of 4:
- We need to consider the pairs of numbers from two dice that sum to 4. These pairs are:
- (1, 3)
- (2, 2)
- (3, 1)
Since order does not matter, we will consider (3, 1) and (1, 3) only once.
2. Frequency of Relevant Outcomes:
- From the given frequency table:
- Frequency of (1, 3) = 5
- Frequency of (2, 2) = 10
3. Total Frequency for Sum of 4:
- Add the frequencies of the outcomes that sum to 4:
[tex]\[
\text{frequency\_sum\_of\_4} = 5 + 10 = 15
\][/tex]
4. Calculate Total Number of Rolls:
- Sum all the frequencies in the table to get the total number of rolls:
[tex]\[
\text{total\_rolls} = 9 + 8 + 10 + 5 + 7 + 8 = 47
\][/tex]
5. Calculate the Experimental Probability:
- The experimental probability is the frequency of the desired outcome divided by the total number of rolls:
[tex]\[
\text{experimental\_probability} = \frac{\text{frequency\_sum\_of\_4}}{\text{total\_rolls}} = \frac{15}{47}
\][/tex]
6. Verify the Answer in Fraction Form:
- The correct fraction for the experimental probability is:
[tex]\[
\frac{15}{47}
\][/tex]
### Conclusion:
The experimental probability of rolling two numbers that sum to 4 is [tex]\(\frac{15}{47}\)[/tex]. This corresponds to one of the given choices, verifying that the right answer is indeed [tex]\(\frac{15}{47}\)[/tex].
