Which of the following can not be the probability of an event?
(i) `(2)/(7)` (ii) 3.8 (iii) 37% (iv) `-0.8` (v) 0.8 (vi) `(-2)/(5)` (vii) `(7)/(8)`

Answer

To determine which of the given options cannot be the probability of an event, we need to recall the fundamental properties of probability. The probability of an event is a number that must satisfy the following conditions:

1. The probability must be between 0 and 1, inclusive. This means:
- It cannot be less than 0.
- It cannot be greater than 1.

Now, let's analyze each option:

1. **(i) \( \frac{2}{7} \)**:
- This is a fraction that equals approximately 0.2857.
- Since \( 0 \leq \frac{2}{7} \leq 1 \), this can be a probability.

2. **(ii) 3.8**:
- This is greater than 1.
- Since \( 3.8 > 1 \), this cannot be a probability.

3. **(iii) 37%**:
- This is equivalent to \( \frac{37}{100} \) or 0.37.
- Since \( 0 \leq 0.37 \leq 1 \), this can be a probability.

4. **(iv) -0.8**:
- This is a negative number.
- Since \( -0.8 < 0 \), this cannot be a probability.

5. **(v) 0.8**:
- This is between 0 and 1.
- Since \( 0 \leq 0.8 \leq 1 \), this can be a probability.

6. **(vi) \( -\frac{2}{5} \)**:
- This is also a negative number.
- Since \( -\frac{2}{5} < 0 \), this cannot be a probability.

7. **(vii) \( \frac{7}{8} \)**:
- This is a fraction that equals 0.875.
- Since \( 0 \leq \frac{7}{8} \leq 1 \), this can be a probability.

Now, summarizing the options that cannot be probabilities:
- (ii) 3.8
- (iv) -0.8
- (vi) \( -\frac{2}{5} \)

Thus, the final answer is that the options that cannot be the probability of an event are (ii), (iv), and (vi).