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To determine if the given table represents a probability distribution, we need to verify two conditions:

1. **Non-negative probabilities**: All the values of \( P(x) \) must be between 0 and 1, inclusive.
2. **Sum of probabilities equals 1**: The total of all \( P(x) \) values must add up to 1.

Let's check these conditions for the provided table:

| \( x \) | \( P(x) \) |
|--------|------------|
| 0      | 0          |
| 1      | 0.25       |
| 2      | 0.15       |
| 3      | 0.6        |

1. **Non-negative probabilities**: All \( P(x) \) values are between 0 and 1, so the first condition is satisfied.

2. **Sum of probabilities**:
   \[
   0 + 0.25 + 0.15 + 0.6 = 1
   \]
   The sum is exactly 1, so the second condition is also satisfied.

### Conclusion:
Yes, this table **does** represent a probability distribution.

Would you like further explanation or details?

Here are 5 related questions you might find helpful:
1. What other types of probability distributions exist?
2. How can probability distributions be used in real-world scenarios?
3. What is the difference between discrete and continuous probability distributions?
4. How do you calculate the expected value of a probability distribution?
5. What are the properties of a binomial probability distribution?

**Tip:** When checking for a valid probability distribution, always ensure that the sum of all probabilities equals exactly 1!

Determine whether this table represents a probability distribution: x = {0, 1, 2, 3}, P(x) = {0, 0.25, 0.15, 0.6}

Learn how to determine whether a given table represents a probability distribution by verifying non-negative probabilities and ensuring that the sum of probabilities equals 1. The example uses the values x = {0, 1, 2, 3} and P(x) = {0, 0.25, 0.15, 0.6}, with detailed explanations for Grades 10-12.

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