Answer :
Let's analyze the probabilities step-by-step based on the information provided in the question.
### Experimental Probability:
1. Total number of rolls: 60
2. Number of times a 2 was rolled: 15
The experimental probability is the ratio of the number of successful outcomes (rolling a 2) to the total number of trials (total rolls).
[tex]\[ \text{Experimental Probability} = \frac{\text{Number of times a 2 is rolled}}{\text{Total number of rolls}} = \frac{15}{60} = \frac{1}{4} \][/tex]
So, the experimental probability of rolling a 2 is [tex]\(\frac{1}{4}\)[/tex].
### Theoretical Probability:
1. A fair six-sided number cube has 6 faces, each equally likely to come up.
2. There is 1 face with the number 2 on it.
The theoretical probability is the ratio of the number of favorable outcomes (rolling a 2) to the total number of possible outcomes (total faces on the cube).
[tex]\[ \text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6} \][/tex]
So, the theoretical probability of rolling a 2 is [tex]\(\frac{1}{6}\)[/tex].
Given these calculations:
- The experimental probability of rolling a 2 is [tex]\(\frac{1}{4}\)[/tex].
- The theoretical probability of rolling a 2 is [tex]\(\frac{1}{6}\)[/tex].
Thus, the correct statement is:
The experimental probability of rolling a 2 is [tex]\(\frac{1}{4}\)[/tex] and the theoretical probability of rolling a 2 is [tex]\(\frac{1}{6}\)[/tex].
### Experimental Probability:
1. Total number of rolls: 60
2. Number of times a 2 was rolled: 15
The experimental probability is the ratio of the number of successful outcomes (rolling a 2) to the total number of trials (total rolls).
[tex]\[ \text{Experimental Probability} = \frac{\text{Number of times a 2 is rolled}}{\text{Total number of rolls}} = \frac{15}{60} = \frac{1}{4} \][/tex]
So, the experimental probability of rolling a 2 is [tex]\(\frac{1}{4}\)[/tex].
### Theoretical Probability:
1. A fair six-sided number cube has 6 faces, each equally likely to come up.
2. There is 1 face with the number 2 on it.
The theoretical probability is the ratio of the number of favorable outcomes (rolling a 2) to the total number of possible outcomes (total faces on the cube).
[tex]\[ \text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6} \][/tex]
So, the theoretical probability of rolling a 2 is [tex]\(\frac{1}{6}\)[/tex].
Given these calculations:
- The experimental probability of rolling a 2 is [tex]\(\frac{1}{4}\)[/tex].
- The theoretical probability of rolling a 2 is [tex]\(\frac{1}{6}\)[/tex].
Thus, the correct statement is:
The experimental probability of rolling a 2 is [tex]\(\frac{1}{4}\)[/tex] and the theoretical probability of rolling a 2 is [tex]\(\frac{1}{6}\)[/tex].
