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.
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.
Answers
GPT-4o mini
To compare the experimental probability with the theoretical probability, let's calculate both.
1. **Theoretical Probability**: When rolling a fair six-sided die, the probability of rolling any specific number (like a 1) is given by:
\( \text{Theoretical Probability} = \frac{1}{6} \).
2. **Experimental Probability**: The experimental probability is calculated based on the results of the experiment. In this case:
- The number of times a 1 was rolled = 8
- Total rolls = 60
Thus, the experimental probability of rolling a 1 is:
\[
\text{Experimental Probability} = \frac{8}{60} = \frac{2}{15} \approx 0.1333.
\]
3. **Comparison**: Now, let's compare both probabilities:
- Theoretical Probability = \( \frac{1}{6} \approx 0.1667 \).
- Experimental Probability = \( \frac{2}{15} \approx 0.1333 \).
Since \( \frac{2}{15} < \frac{1}{6} \), we can conclude that:
**The experimental probability (8/60) is less than the theoretical probability (1/6).**
1. **Theoretical Probability**: When rolling a fair six-sided die, the probability of rolling any specific number (like a 1) is given by:
\( \text{Theoretical Probability} = \frac{1}{6} \).
2. **Experimental Probability**: The experimental probability is calculated based on the results of the experiment. In this case:
- The number of times a 1 was rolled = 8
- Total rolls = 60
Thus, the experimental probability of rolling a 1 is:
\[
\text{Experimental Probability} = \frac{8}{60} = \frac{2}{15} \approx 0.1333.
\]
3. **Comparison**: Now, let's compare both probabilities:
- Theoretical Probability = \( \frac{1}{6} \approx 0.1667 \).
- Experimental Probability = \( \frac{2}{15} \approx 0.1333 \).
Since \( \frac{2}{15} < \frac{1}{6} \), we can conclude that:
**The experimental probability (8/60) is less than the theoretical probability (1/6).**