Let X represent the difference between number of heads and number of tails obtained when a coin is tossed 6 times. What are possible values of X?

Answer

To find the possible values of \( X \), which represents the difference between the number of heads and the number of tails when a coin is tossed 6 times, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
When a coin is tossed 6 times, the outcomes can be heads (H) or tails (T). Let \( H \) be the number of heads and \( T \) be the number of tails. We know that \( H + T = 6 \).

2. **Define \( X \)**:
The difference \( X \) can be defined as:
\[ X = H - T \]

3. **Express \( T \) in terms of \( H \)**:
Since \( T = 6 - H \), we can substitute \( T \) in the equation for \( X \):
\[ X = H - (6 - H) = H - 6 + H = 2H - 6 \]

4. **Determine the Range of \( H \)**:
The number of heads \( H \) can take values from 0 to 6 (inclusive). Therefore, the possible values for \( H \) are:
\[ H = 0, 1, 2, 3, 4, 5, 6 \]

5. **Calculate Possible Values of \( X \)**:
Now we can calculate \( X \) for each value of \( H \):
- If \( H = 0 \):
\[ X = 2(0) - 6 = -6 \]
- If \( H = 1 \):
\[ X = 2(1) - 6 = -4 \]
- If \( H = 2 \):
\[ X = 2(2) - 6 = -2 \]
- If \( H = 3 \):
\[ X = 2(3) - 6 = 0 \]
- If \( H = 4 \):
\[ X = 2(4) - 6 = 2 \]
- If \( H = 5 \):
\[ X = 2(5) - 6 = 4 \]
- If \( H = 6 \):
\[ X = 2(6) - 6 = 6 \]

6. **List the Possible Values of \( X \)**:
The possible values of \( X \) are:
\[ -6, -4, -2, 0, 2, 4, 6 \]

### Conclusion:
The possible values of \( X \) when a coin is tossed 6 times are:
\[ -6, -4, -2, 0, 2, 4, 6 \]