To determine which of the given values is not a possible value for a probability, we need to understand the fundamental property of probabilities. Probability values must be between 0 and 1 inclusive. This means any valid probability must satisfy [tex]\(0 \leq \text{probability} \leq 1\)[/tex].
Let's evaluate each of the given options:
Option A: [tex]\( \frac{1}{16} \)[/tex]
This fraction simplifies to a decimal as follows:
[tex]\[ \frac{1}{16} = 0.0625 \][/tex]
Since [tex]\(0.0625\)[/tex] is between 0 and 1, it is a valid probability value.
Option B: 0.001
This is already in decimal form and:
[tex]\[ 0.001 \][/tex]
Since [tex]\(0.001\)[/tex] is between 0 and 1, it is a valid probability value.
Option C: [tex]\( \frac{5}{4} \)[/tex]
This fraction can be converted to a decimal by dividing 5 by 4:
[tex]\[ \frac{5}{4} = 1.25 \][/tex]
Since [tex]\(1.25\)[/tex] is greater than 1, it is not a valid probability value.
Option D: 0.82
This is already in decimal form and:
[tex]\[ 0.82 \][/tex]
Since [tex]\(0.82\)[/tex] is between 0 and 1, it is a valid probability value.
Based on the evaluations above, the option that is not a possible value for a probability is:
Option C: [tex]\( \frac{5}{4} \)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
