To determine which of the given values could be a probability, we need to remember that probabilities must lie within the range of 0 to 1 inclusive. This means any valid probability must be between and including 0 and 1.
Let's evaluate each given value:
1. [tex]\(\frac{5}{4}\)[/tex]:
- [tex]\(\frac{5}{4} = 1.25\)[/tex]
- Since [tex]\(1.25\)[/tex] is greater than [tex]\(1\)[/tex], it cannot be a probability.
2. [tex]\(\frac{23}{75}\)[/tex]:
- [tex]\(\frac{23}{75} \approx 0.30666666666666664\)[/tex]
- This is a valid probability because it is between [tex]\(0\)[/tex] and [tex]\(1\)[/tex].
3. [tex]\(0\)[/tex]:
- [tex]\(0\)[/tex] is a valid probability as it represents the event that is impossible and falls within the range of [tex]\(0 \leq p \leq 1\)[/tex].
4. [tex]\(\frac{-3}{4}\)[/tex]:
- [tex]\(\frac{-3}{4} = -0.75\)[/tex]
- Since [tex]\(-0.75\)[/tex] is less than [tex]\(0\)[/tex], it cannot be a probability.
5. [tex]\(1\)[/tex]:
- [tex]\(1\)[/tex] is a valid probability as it represents the event that is certain and falls within the range of [tex]\(0 \leq p \leq 1\)[/tex].
Based on these evaluations, the values that could be a probability are:
[tex]\[
\frac{23}{75}, \; 0, \; 1
\][/tex]
So, the correct answer includes:
[tex]\(\frac{23}{75}\)[/tex], 0, and 1.
