To determine which value cannot represent the probability of an event occurring, we need to understand the properties of probabilities.
Probabilities are measures of the likelihood of an event occurring and must fall within the range from 0 to 1, inclusive. This means that any valid probability will be a number between 0 (impossible event) and 1 (certain event).
Let's examine each given value:
1. [tex]\(\frac{1}{100}\)[/tex]:
- This fraction equals 0.01 when converted to a decimal.
- 0.01 is within the range of 0 to 1.
- Therefore, [tex]\(\frac{1}{100}\)[/tex] can represent a probability.
2. 0.29:
- This number is already in decimal form.
- 0.29 is within the range of 0 to 1.
- Therefore, 0.29 can represent a probability.
3. 85%:
- Percentages must be converted to a decimal for comparison. [tex]\(85\%\)[/tex] is equivalent to [tex]\(\frac{85}{100} = 0.85\)[/tex].
- 0.85 is within the range of 0 to 1.
- Therefore, [tex]\(85\%\)[/tex] can represent a probability.
4. [tex]\(\frac{3}{2}\)[/tex]:
- This fraction equals 1.5 when converted to a decimal.
- 1.5 is outside the range of 0 to 1.
- Therefore, [tex]\(\frac{3}{2}\)[/tex] cannot represent a probability.
Summary:
- [tex]\(\frac{1}{100}\)[/tex] = 0.01 (valid probability)
- 0.29 (valid probability)
- [tex]\(85\%\)[/tex] = 0.85 (valid probability)
- [tex]\(\frac{3}{2}\)[/tex] = 1.5 (invalid probability)
The value that cannot represent the probability of an event occurring is [tex]\(\frac{3}{2}\)[/tex].
