Let's analyze the problem step by step.
1. Theoretical Probability:
- A six-sided, fair number cube has equal probabilities for each face (number) to appear.
- The probability of rolling any particular number (e.g., 3) is the number of favorable outcomes (rolling a 3) divided by the total number of outcomes (6 faces).
- Therefore, the theoretical probability [tex]\( P(\text{rolling a 3}) \)[/tex] is [tex]\( \frac{1}{6} \)[/tex].
2. Experimental Probability:
- The experimental probability is calculated based on the observed data from an experiment.
- In this case, the number 3 appeared 20 times out of 100 rolls.
- The experimental probability [tex]\( P(\text{rolling a 3}) \)[/tex] is the frequency of rolling a 3 divided by the total number of rolls: [tex]\( \frac{20}{100} = \frac{1}{5} \)[/tex].
3. Comparing Probabilities:
- The theoretical probability, based on the fairness of the die, is [tex]\( \frac{1}{6} \)[/tex].
- The experimental probability, based on the results of this specific experiment, is [tex]\( \frac{1}{5} \)[/tex].
Given this information, the correct statement about rolling a 3 is:
- The theoretical probability is 1/6. The experimental probability is 1/5.
Therefore, the correct answer is the third option:
- The theoretical probability is 1/6. The experimental probability is 1/5.
