The probability that cannot exist among the following:

Options

A. `2/3`
B. `-1.5`
C. `15%`
D. 0.7

Answer

To determine which of the given probabilities cannot exist, we need to analyze each option based on the fundamental properties of probability.

### Step-by-Step Solution:

1. **Understand the Definition of Probability**:
Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes. It must always lie between 0 and 1, inclusive. This means:
\[ 0 \leq P \leq 1 \]

2. **Evaluate Option 1: \( \frac{2}{3} \)**:
- Convert \( \frac{2}{3} \) to decimal: \( \frac{2}{3} \approx 0.67 \).
- Since \( 0.67 \) is between 0 and 1, this probability is valid.
- **Conclusion**: Option 1 can exist.

3. **Evaluate Option 2: \( -1.5 \)**:
- This value is negative.
- Since probabilities cannot be negative, this option does not satisfy the condition \( 0 \leq P \leq 1 \).
- **Conclusion**: Option 2 cannot exist.

4. **Evaluate Option 3: \( 15\% \)**:
- Convert \( 15\% \) to decimal: \( 15\% = \frac{15}{100} = 0.15 \).
- Since \( 0.15 \) is between 0 and 1, this probability is valid.
- **Conclusion**: Option 3 can exist.

5. **Evaluate Option 4: \( 0.7 \)**:
- This value is already in decimal form.
- Since \( 0.7 \) is between 0 and 1, this probability is valid.
- **Conclusion**: Option 4 can exist.

### Final Conclusion:
The only option that does not represent a valid probability is **Option 2: \( -1.5 \)**.

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