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?
(4 Points)

The experimental probability (8/60) is less than the theoretical probability (1/6).

The experimental probability (8/60) is equal to the theoretical probability (1/6).

The experimental probability (8/60) is greater than the theoretical probability (1/6).

There is no way to compare experimental and theoretical probability.

Answer 1

To compare the experimental probability of rolling a 1 to the theoretical probability, we need to calculate both probabilities.

1. **Theoretical Probability**:
A six-sided die has an equal chance of landing on any one of its sides. The theoretical probability of rolling a 1 is:

\[
P(\text{rolling a 1}) = \frac{1 \text{ (favorable outcome)}}{6 \text{ (total outcomes)}} = \frac{1}{6} \approx 0.1667
\]

2. **Experimental Probability**:
The experimental probability is calculated based on the results of the experiment. The die rolled a 1 a total of 8 times out of 60 rolls. Thus, the experimental probability is:

\[
P(\text{rolling a 1}) = \frac{8 \text{ (times 1 was rolled)}}{60 \text{ (total rolls)}} = \frac{8}{60} = \frac{2}{15} \approx 0.1333
\]

3. **Comparison**:
- The experimental probability is \(\frac{2}{15} \approx 0.1333\).
- The theoretical probability is \(\frac{1}{6} \approx 0.1667\).

Now, comparing the two:

\[
\frac{2}{15} < \frac{1}{6}
\]

Therefore, the correct answer is:

**The experimental probability (8/60) is less than the theoretical probability (1/6).**