To determine the probability that Ethan rolls a number greater than 2 on a 6-sided number cube, we can follow these steps:
1. Identify the total number of possible outcomes:
A standard 6-sided number cube (die) has 6 faces, numbered 1 through 6. Therefore, the total number of possible outcomes when rolling the cube is 6.
2. Identify the number of favorable outcomes:
We are interested in rolling a number greater than 2. The numbers greater than 2 on the cube are 3, 4, 5, and 6. Thus, there are 4 favorable outcomes.
3. Calculate the probability:
Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Hence, the probability [tex]\( P \)[/tex] can be calculated as:
[tex]\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
Substituting the values:
[tex]\[
P = \frac{4}{6}
\][/tex]
4. Simplify the fraction:
We can simplify [tex]\(\frac{4}{6}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}
\][/tex]
Therefore, the probability that Ethan rolls a number greater than 2 on a 6-sided number cube is [tex]\(\frac{2}{3}\)[/tex].
The correct answer is A. [tex]\(\frac{2}{3}\)[/tex].
