Descibe the sample space :
A coin is tossed twice . If it results in a head , a die is thrown , otherwise a coin is tossed .

Answer

To describe the sample space for the given scenario, we will break down the steps clearly.

### Step-by-Step Solution:

1. **Toss the Coin Twice**:
When a coin is tossed twice, the possible outcomes are:
- Head (H), Head (H) → HH
- Head (H), Tail (T) → HT
- Tail (T), Head (H) → TH
- Tail (T), Tail (T) → TT
So, the outcomes from tossing the coin twice are: {HH, HT, TH, TT}.

2. **Determine the Next Action Based on the Coin Toss**:
- If the result includes at least one Head (H), we will throw a die.
- If the result is Tail (T) only, we will toss the coin again.

3. **Outcomes When a Die is Thrown**:
- For HH: Since there are two heads, we throw a die. The outcomes will be:
- HH1, HH2, HH3, HH4, HH5, HH6 (where the number represents the die result).
- For HT: Since there is one head, we also throw a die. The outcomes will be:
- HT1, HT2, HT3, HT4, HT5, HT6.
- For TH: Similar to HT, we throw a die. The outcomes will be:
- TH1, TH2, TH3, TH4, TH5, TH6.

4. **Outcomes When the Coin is Tossed Again**:
- For TT: Since there are no heads, we toss the coin again. The possible outcomes from tossing the coin again are:
- Head (H), Head (H) → HH
- Head (H), Tail (T) → HT
- Tail (T), Head (H) → TH
- Tail (T), Tail (T) → TT
Thus, the outcomes will be: {HH, HT, TH, TT}.

5. **Combine All Outcomes**:
Now we combine all the outcomes based on the previous steps:
- From HH: {HH1, HH2, HH3, HH4, HH5, HH6}
- From HT: {HT1, HT2, HT3, HT4, HT5, HT6}
- From TH: {TH1, TH2, TH3, TH4, TH5, TH6}
- From TT: {HH, HT, TH, TT} (the outcomes from the second toss)

### Final Sample Space:
The complete sample space is:
- {HH1, HH2, HH3, HH4, HH5, HH6, HT1, HT2, HT3, HT4, HT5, HT6, TH1, TH2, TH3, TH4, TH5, TH6, HH, HT, TH, TT}