Let's analyze the given data and interpret the results step-by-step. The table provides the frequency of each number rolled on a number cube.
| Number Rolled | Frequency |
|---------------|-----------|
| 1 | 11 |
| 2 | 16 |
| 3 | 14 |
| 4 | 20 |
| 5 | 12 |
| 6 | 17 |
First, we calculate the total number of rolls:
Total rolls = 11 + 16 + 14 + 20 + 12 + 17 = 90
Next, let's find the relative frequency of rolling a 4:
Relative frequency of rolling a 4 = Frequency of 4 / Total rolls
= 20 / 90
= 0.2222222222222222
Converting 0.2222222222222222 to a fraction, we get:
0.2222222222222222 = 2/9
So, the relative frequency of rolling a 4 is indeed [tex]\( \frac{2}{9} \)[/tex].
Now, let's move on to the experimental probability of rolling a 3:
Experimental probability of rolling a 3 = Frequency of 3 / Total rolls
= 14 / 90
= 0.15555555555555556
The theoretical probability of rolling any specific number on a fair six-sided die (number cube) is calculated as:
Theoretical probability of rolling a specific number = 1 / 6
= 0.16666666666666666
Finally, we compare the experimental probability of rolling a 3 to the theoretical probability:
0.15555555555555556 (experimental) < 0.16666666666666666 (theoretical)
Thus, the experimental probability of rolling a 3 is not greater than the theoretical probability of rolling a 3.
Summarizing the results:
1. The relative frequency of rolling a 4 is [tex]\( \frac{2}{9} \)[/tex].
2. The experimental probability of rolling a 3 is not greater than the theoretical probability of rolling a 3.
Based on the analysis, it seems like these are the most relevant and true statements for this situation:
- The relative frequency of rolling a 4 is [tex]\( \frac{2}{9} \)[/tex].
- The experimental probability of rolling a 3 is not greater than the theoretical probability of rolling a 3.
