To compare the experimental probability of rolling a 1 to the theoretical probability, we need to first calculate both probabilities.
Theoretical Probability: For a fair six-sided die, the theoretical probability of rolling a 1 is:
\[ P(1) = \frac{1}{6} \]
Experimental Probability: The experimental probability is calculated based on the results of the 60 rolls. The number of times a 1 was rolled is 8. Therefore, the experimental probability of rolling a 1 is:
\[ P_{\text{experimental}}(1) = \frac{\text{Number of times 1 was rolled}}{\text{Total number of rolls}} = \frac{8}{60} \]
Calculating \(\frac{8}{60}\):
\[ P_{\text{experimental}}(1) = \frac{8}{60} = \frac{2}{15} \approx 0.1333 \]
Comparison: Now we can compare the two probabilities:
- Theoretical Probability: \(P(1) = \frac{1}{6} \approx 0.1667\)
- Experimental Probability: \(P_{\text{experimental}}(1) = \frac{2}{15} \approx 0.1333\)
Conclusion: The experimental probability of rolling a 1 (\(0.1333\)) is lower than the theoretical probability (\(0.1667\)).