To determine the probability that Ethan rolls a number greater than 2 on a 6-sided number cube, let's walk through the problem step-by-step.
1. Identify the total number of possible outcomes:
- A 6-sided number cube has 6 faces, each numbered from 1 to 6.
- Therefore, there are 6 possible outcomes: 1, 2, 3, 4, 5, and 6.
2. Identify the favorable outcomes:
- We are looking for the probability of rolling a number greater than 2.
- The numbers greater than 2 on a 6-sided number cube are: 3, 4, 5, and 6.
- So, there are 4 favorable outcomes.
3. Calculate the probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- Here, the number of favorable outcomes is 4, and the total number of possible outcomes is 6.
- Thus, the probability [tex]\( P \)[/tex] is given by:
[tex]\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{6}
\][/tex]
4. Simplify the fraction:
- [tex]\(\frac{4}{6}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
Therefore, the probability that Ethan rolls a number greater than 2 is [tex]\(\frac{2}{3}\)[/tex].
So, the correct answer is:
A. [tex]\(\frac{2}{3}\)[/tex]
