There are 5 red and 2 black balls in a bag. Two balls are drawn at random. If `X` denotes the number of black balls, what are the possible values of `X`?

Explanation

To solve the problem, we need to determine the possible values of \( X \), where \( X \) denotes the number of black balls drawn when two balls are drawn at random from a bag containing 5 red balls and 2 black balls.

### Step-by-Step Solution:

1. **Identify the Total Number of Balls**:
- There are 5 red balls and 2 black balls in the bag.
- Total number of balls = 5 (red) + 2 (black) = 7 balls.

2. **Define the Random Variable \( X \)**:
- \( X \) represents the number of black balls drawn when two balls are drawn.
- The possible values of \( X \) can be 0, 1, or 2, depending on how many black balls are drawn.

3. **Determine the Possible Outcomes**:
- When drawing 2 balls, the possible combinations concerning the number of black balls are:
- **0 black balls**: This means both balls drawn are red.
- **1 black ball**: This means one ball is black and the other is red.
- **2 black balls**: This means both balls drawn are black.

4. **List the Possible Values of \( X \)**:
- From the combinations above, we can conclude:
- If 0 black balls are drawn, \( X = 0 \).
- If 1 black ball is drawn, \( X = 1 \).
- If 2 black balls are drawn, \( X = 2 \).

5. **Conclusion**:
- The possible values of \( X \) are \( 0, 1, \) and \( 2 \).

### Final Answer:
The possible values of \( X \) are \( \{0, 1, 2\} \).