To determine which value cannot represent the probability of an event occurring, we need to understand the fundamental properties of probabilities.
Probabilities must lie within the range from 0 to 1, inclusive. Let's analyze each given value to see if it falls within this range:
1. [tex]\(\frac{1}{100}\)[/tex]:
- Convert this fraction to a decimal to better understand its value.
- [tex]\(\frac{1}{100} = 0.01\)[/tex].
- Since [tex]\(0.01\)[/tex] is between 0 and 1, this is a valid probability.
2. 0.29:
- This is already in decimal form.
- 0.29 is between 0 and 1, so this is a valid probability.
3. [tex]\(85\%\)[/tex]:
- Convert the percentage to a decimal by dividing by 100.
- [tex]\(85\% = \frac{85}{100} = 0.85\)[/tex].
- Since [tex]\(0.85\)[/tex] is between 0 and 1, this is a valid probability.
4. [tex]\(\frac{3}{2}\)[/tex]:
- Convert this fraction to a decimal to better understand its value.
- [tex]\(\frac{3}{2} = 1.5\)[/tex].
- Since 1.5 is greater than 1, this is not a valid probability.
Thus, the value that cannot represent the probability of an event occurring is [tex]\(\frac{3}{2}\)[/tex].
In conclusion, [tex]\(\frac{3}{2}\)[/tex] (option 4) is the value that cannot represent a probability.
