Describe the Sample Space for the experiment:
A coin is tossed repeatedly until a tail comes up.

Answer

To describe the sample space for the experiment where a coin is tossed repeatedly until a tail comes up, we need to consider all the possible outcomes of this experiment.

### Step-by-Step Solution:

1. **Understanding the Experiment**:
- We are tossing a coin repeatedly.
- The experiment continues until we get a tail (T).
- Each toss can result in either a head (H) or a tail (T).

2. **Identifying Possible Outcomes**:
- The first possible outcome is getting a tail on the first toss: **T**.
- If we get a head on the first toss, we will toss again. The second possible outcome could be either:
- Getting a tail on the second toss: **HT**.
- Getting another head on the second toss, leading to a third toss: **HH**.
- If we get a tail on the third toss: **HHT**.
- If we get another head on the third toss, we continue: **HHH**.
- If we finally get a tail on the fourth toss: **HHHT**.
- This pattern continues indefinitely.

3. **Formulating the Sample Space**:
- The sample space (S) can be expressed as:
- S = { T, HT, HHT, HHH, HHHH, ... }
- This means the sample space includes:
- A single tail (T).
- A sequence of heads followed by a tail (HT, HHT, HHH, HHHH, ...).

4. **Conclusion**:
- The sample space consists of all sequences of heads followed by a tail, where the number of heads can be zero or more.

### Final Sample Space:
- S = { T, HT, HHT, HHH, HHHH, ... }