Which of the following cannot be the probability of an event?

Options

A. `(1)/(3)`
B. 0.1
C. 0.333
D. `(17)/(16)`

Explanation

To determine which of the given options cannot be the probability of an event, we need to remember that the probability of an event must always lie between 0 and 1, inclusive. This means that:

- The minimum probability is 0 (impossible event).
- The maximum probability is 1 (certain event).

Now, let's analyze each option step by step:

1. **Option A: \( \frac{1}{3} \)**
- Convert \( \frac{1}{3} \) to decimal:
\[ \frac{1}{3} \approx 0.333 \]
- Check if \( 0.333 \) is between 0 and 1:
- \( 0 < 0.333 < 1 \)
- Conclusion: This can be a probability.

2. **Option B: \( 0.1 \)**
- Check if \( 0.1 \) is between 0 and 1:
- \( 0 < 0.1 < 1 \)
- Conclusion: This can also be a probability.

3. **Option C: \( 3\% \)**
- Convert \( 3\% \) to decimal:
\[ 3\% = \frac{3}{100} = 0.03 \]
- Check if \( 0.03 \) is between 0 and 1:
- \( 0 < 0.03 < 1 \)
- Conclusion: This can also be a probability.

4. **Option D: \( \frac{17}{16} \)**
- Convert \( \frac{17}{16} \) to decimal:
\[ \frac{17}{16} = 1.0625 \]
- Check if \( 1.0625 \) is between 0 and 1:
- \( 1.0625 > 1 \)
- Conclusion: This cannot be a probability.

Thus, the option that cannot be the probability of an event is **Option D: \( \frac{17}{16} \)**.