To determine the probability of rolling a vowel when a cube with letters [tex]\( A, B, C, D, E, \)[/tex] and [tex]\( F \)[/tex] is rolled, you can follow these steps:
1. Identify the total number of sides on the cube:
The cube is a standard six-sided die with each side marked by a unique letter from the set [tex]\(\{A, B, C, D, E, F\}\)[/tex]. Therefore, the total number of sides is [tex]\(6\)[/tex].
2. Identify the number of vowels on the cube:
In the set of letters, [tex]\(A\)[/tex] and [tex]\(E\)[/tex] are the only vowels. So, we have [tex]\(2\)[/tex] vowels in this case.
3. Calculate the probability of rolling a vowel:
Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Here, the favorable outcomes are rolling either 'A' or 'E'.
So, the probability [tex]\(P\)[/tex] of rolling a vowel can be computed by:
[tex]\[
P(\text{vowel}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{2}{6}
\][/tex]
4. Simplify the fraction:
Simplifying [tex]\(\frac{2}{6}\)[/tex] gives:
[tex]\[
\frac{2}{6} = \frac{1}{3}
\][/tex]
Therefore, the probability of rolling a vowel [tex]\(A\)[/tex] or [tex]\(E\)[/tex] is [tex]\(\frac{1}{3}\)[/tex].
So the correct answer is:
[tex]\[
\boxed{\frac{1}{3}}
\][/tex]
