Which of the following numerical expressions may represent the probability of a simple event?

A. [tex]\(\frac{1}{6}\)[/tex]

B. [tex]\(\frac{11}{6}\)[/tex]

C. [tex]\(\frac{1}{6} + \frac{1}{5}\)[/tex]

D. [tex]\(\frac{1}{6} + \frac{1}{2}\)[/tex]



Answer :

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]

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