Let's analyze each option to determine if it could represent the probability of a simple event.
### Option A: [tex]\(\frac{1}{6}\)[/tex]
To find the value of [tex]\(\frac{1}{6}\)[/tex], we divide 1 by 6.
[tex]\[
\frac{1}{6} \approx 0.1667
\][/tex]
This value is between 0 and 1, which makes it a valid probability.
### Option B: [tex]\(\frac{1.1}{6}\)[/tex]
To find the value of [tex]\(\frac{1.1}{6}\)[/tex], we divide 1.1 by 6.
[tex]\[
\frac{1.1}{6} \approx 0.1833
\][/tex]
Though this value is between 0 and 1, it represents a probability calculation and needs to be strictly accurate in the context of simple events. Typically, [tex]\(1.1\)[/tex] is an unusual numerator for a simple event probability, hence it might be considered not valid. However, numerically it is within the acceptable range of probability values.
### Option C: [tex]\(\frac{1}{6} + \frac{1}{5}\)[/tex]
First, we calculate [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[
\frac{1}{6} \approx 0.1667
\][/tex]
Next, we calculate [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[
\frac{1}{5} = 0.2
\][/tex]
Adding these together:
[tex]\[
0.1667 + 0.2 = 0.3667
\][/tex]
This value is between 0 and 1, making it a valid probability.
### Option D: [tex]\(\frac{1}{6} + \frac{1}{2}\)[/tex]
First, we calculate [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[
\frac{1}{6} \approx 0.1667
\][/tex]
Next, we calculate [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
Adding these together:
[tex]\[
0.1667 + 0.5 = 0.6667
\][/tex]
This value is between 0 and 1, making it a valid probability.
### Conclusion:
Among the given options, the correct numerical expression that represents the probability of a simple event is [tex]\(\frac{1}{6}\)[/tex]. Hence, the correct answer is:
A. [tex]\(\frac{1}{6}\)[/tex]
