A coin will be tossed wine, and each Tara will be recorded as heads (H) or tails (T). Give this sample space describing all possible outcomes. Then give all of the outcomes for the event that the first toss is tails.  Use the  format HT to mean that the first toss is heads and the second is tails. If there is more than one element in the set, separate them with commas.

Let's break down the problem step by step.

### 1. Sample Space
If a coin is tossed twice, the sample space includes all possible outcomes from those two tosses. Each toss can result in either heads (H) or tails (T).

So, the sample space \( S \) is:

\[
S = \{ HH, HT, TH, TT \}
\]

### 2. Outcomes where the First Toss is Tails
Now, we're interested in the event where the first toss is tails (T). The second toss can be either heads (H) or tails (T), so the outcomes for this event are:

\[
\text{Event } E = \{ TH, TT \}
\]

### Summary:
- **Sample Space \( S \)**: \( \{ HH, HT, TH, TT \} \)
- **Outcomes where the First Toss is Tails**: \( \{ TH, TT \} \)

Would you like more details or have any further questions?

Here are some related questions you might find interesting:
1. What is the probability of getting exactly one head in two tosses?
2. How would the sample space change if the coin is tossed three times?
3. What is the probability of getting two heads in two tosses?
4. How many outcomes would there be if the coin was tossed three times instead of two?
5. What is the probability that both tosses result in the same outcome?
6. How does the probability change if the coin is biased?
7. Can you generalize the sample space for \( n \) tosses of a coin?
8. What would be the sample space if a die is tossed twice instead of a coin?

**Tip:** Always start by defining the sample space when solving probability problems. This helps to clearly identify all possible outcomes before calculating probabilities.

Explore the concept of coin toss probability with a focus on sample space and specific events. Learn how to analyze outcomes when the first toss is tails. Suitable for Grades 6-8.

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