Let's analyze the question step-by-step.
1. Calculate the total number of rolls.
Add up all the frequencies:
[tex]\[
11 + 16 + 14 + 20 + 12 + 17 = 90
\][/tex]
So, the total number of rolls is 90.
2. Calculate the relative frequency of rolling a 4.
The frequency of rolling a 4 is 20. Therefore, the relative frequency is:
[tex]\[
\frac{20}{90} \approx 0.2222 \approx \frac{2}{9}
\][/tex]
Therefore, the statement "The relative frequency of rolling a 4 is [tex]\(\frac{2}{9}\)[/tex]" is correct.
3. Calculate the experimental probability of rolling a 3.
The frequency of rolling a 3 is 14. Thus, the experimental probability is:
[tex]\[
\frac{14}{90} \approx 0.1556
\][/tex]
4. Calculate the theoretical probability of rolling any specific number on a fair cube.
A fair number cube (die) has 6 faces, and each face has an equal probability of appearing:
[tex]\[
\frac{1}{6} \approx 0.1667
\][/tex]
5. Compare the experimental probability of rolling a 3 with the theoretical probability.
The experimental probability of rolling a 3 (0.1556) is less than the theoretical probability (0.1667).
Given this information, we can conclude the following:
- The relative frequency of rolling a 4 is [tex]\(\frac{2}{9}\)[/tex]. This statement is correct.
- The experimental probability of rolling a 3 is approximately 0.1556.
- The theoretical probability of rolling any specific number is approximately 0.1667.
- The experimental probability of rolling a 3 is less than the theoretical probability.
Therefore, based on these steps:
- The statement "The relative frequency of rolling a 4 is [tex]\(\frac{2}{9}\)[/tex]" is correct.
- The statement "The experimental probability of rolling a 3 is greater than the theoretical probability of rolling a 3" is incorrect. The experimental probability is less than the theoretical probability.
Considering all steps and calculations, the correct answer should include the statement about the relative frequency of rolling a 4. There is no option provided that is correct, besides the one about the relative frequency of rolling a 4.
