To determine which value cannot represent the probability of an event occurring, we need to recall that probabilities must lie within the range of 0 to 1, inclusive. This means that any valid probability must be a number between 0 and 1.
Now, let's examine each of the given values:
1. [tex]\(\frac{1}{100}\)[/tex]
[tex]\[
\frac{1}{100} = 0.01
\][/tex]
This value falls within the range [0, 1], so it can represent the probability of an event occurring.
2. 0.29
This value is already given in decimal form and falls within the range [0, 1]. It can represent the probability of an event occurring.
3. 85%
To express this percentage as a decimal:
[tex]\[
85\% = \frac{85}{100} = 0.85
\][/tex]
This value falls within the range [0, 1], so it can represent the probability of an event occurring.
4. [tex]\(\frac{3}{2}\)[/tex]
[tex]\[
\frac{3}{2} = 1.5
\][/tex]
This value is greater than 1, which means it falls outside the permissible range for probabilities. Therefore, it cannot represent the probability of an event occurring.
Thus, the value that cannot represent the probability of an event occurring is [tex]\(\frac{3}{2}\)[/tex] or 1.5.
