To address the question of how the experimental probability of rolling a 3 compares with the theoretical probability of rolling a 3, let's go through the detailed steps based on the provided data.
### Step-by-Step Solution:
1. Identify the Number of Times Each Outcome Occurred:
- Outcomes for rolling a 1: 18
- Outcomes for rolling a 2: 16
- Outcomes for rolling a 3: 24
- Outcomes for rolling a 4: 26
- Outcomes for rolling a 5: 16
- Outcomes for rolling a 6: 20
2. Calculate the Total Number of Rolls:
- Total rolls = [tex]\( 18 + 16 + 24 + 26 + 16 + 20 = 120 \)[/tex]
3. Determine the Experimental Probability of Rolling a 3:
- Number of times a 3 was rolled = 24
- Experimental Probability (P_exp) = [tex]\(\frac{\text{Number of times 3 was rolled}}{\text{Total number of rolls}} = \frac{24}{120} = 0.2\)[/tex]
4. Determine the Theoretical Probability of Rolling a 3:
- Theoretical Probability (P_theor) for a fair six-sided die = [tex]\(\frac{1}{6} \approx 0.16666666666666666\)[/tex]
5. Compare the Experimental and Theoretical Probabilities:
- Difference between experimental and theoretical probabilities = [tex]\(0.2 - 0.16666666666666666 = 0.033333333333333354\)[/tex]
6. Express the Difference in Fractional Form:
- The difference in fractional form is [tex]\(\frac{1}{30}\)[/tex]
### Final Comparison:
- The experimental probability of rolling a 3 is [tex]\(\frac{1}{30}\)[/tex] greater than the theoretical probability of rolling a 3.
Therefore, the correct statement is:
- The experimental probability of rolling a 3 is [tex]\(\frac{1}{30}\)[/tex] greater than the theoretical probability of rolling a 3.
