To determine which of the given options are valid ways of showing probability, we need to understand how probabilities can be expressed. Probabilities are typically expressed in one of the following forms:
1. As a percentage between 0% and 100%.
2. As a fraction between 0 and 1.
3. As a decimal between 0 and 1.
Let's evaluate each option provided:
1. [tex]\( 50\% \)[/tex]
- This is a percentage.
- Percentages are commonly used to represent probabilities.
- [tex]\( 50\% \)[/tex] is the same as [tex]\( \frac{1}{2} \)[/tex] which represents a probability.
2. 557
- This is an integer.
- Probabilities cannot be represented by numbers greater than 1 because they must fall within the range from 0 to 1.
- 557 is not a valid way of representing probability.
3. [tex]\( \frac{3}{4} \)[/tex]
- This is a fraction.
- Fractions are commonly used to show probabilities.
- [tex]\( \frac{3}{4} \)[/tex] lies within the proper range for a probability (0 to 1).
4. [tex]\( 1 \times 10^4 \)[/tex]
- This is a scientific notation representing the number 10,000.
- As previously mentioned, probabilities must be between 0 and 1.
- [tex]\( 1 \times 10^4 \)[/tex] is not a valid way of representing probability.
5. [tex]\( 25\% \)[/tex]
- This is a percentage.
- Percentages are valid representations of probabilities.
- [tex]\( 25\% \)[/tex] is the same as [tex]\( \frac{1}{4} \)[/tex] which represents a probability.
6. [tex]\( \frac{2}{4} \)[/tex]
- This is a fraction.
- Fractions are valid representations of probabilities.
- [tex]\( \frac{2}{4} \)[/tex] simplifies to [tex]\( \frac{1}{2} \)[/tex], which represents a probability.
Based on this evaluation, the valid ways of showing probability among the given options are:
- [tex]\( 50\% \)[/tex]
- [tex]\( \frac{3}{4} \)[/tex]
- [tex]\( 25\% \)[/tex]
- [tex]\( \frac{2}{4} \)[/tex]
Therefore, the indices corresponding to these options are:
- 0 (for [tex]\( 50\% \)[/tex])
- 2 (for [tex]\( \frac{3}{4} \)[/tex])
- 4 (for [tex]\( 25\% \)[/tex])
- 5 (for [tex]\( \frac{2}{4} \)[/tex])
Thus, the correct answer is:
[tex]\[ [0, 2, 4, 5] \][/tex]
