Question

A six-sided die is rolled 60 times in an experiment. The results are:


1: 8 times


2: 12 times


3: 10 times


4: 10 times


5: 9 times


6: 11 times


How does the experimental probability of rolling a 1 compare to the theoretical probability?

Answer 1

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 (\(0.1667\)).