The problem shown in the image involves tossing a coin twice and recording the outcomes as heads (H) or tails (T). Let’s work through it step by step:

Sample Space:

When a coin is tossed twice, there are four possible outcomes:

1. Both tosses result in heads (HH).
2. The first toss is heads, and the second toss is tails (HT).
3. The first toss is tails, and the second toss is heads (TH).
4. Both tosses result in tails (TT).

Thus, the sample space is: $\{HH, HT, TH, TT\}$

Event that the First Toss is Tails:

For the event where the first toss is tails, we only consider outcomes where the first position is "T". These outcomes are:

1. The first toss is tails, and the second toss is heads (TH).
2. The first toss is tails, and the second toss is also tails (TT).

Thus, the event where the first toss is tails is: $\{TH, TT\}$

Final Answers:

• Sample space: $\{HH, HT, TH, TT\}$
• Event where the first toss is tails: $\{TH, TT\}$

Would you like further details or have any questions?

Here are 5 related questions you could explore:

1. What is the probability of getting exactly one heads in two tosses?
2. How would the sample space change if the coin is tossed three times instead of two?
3. What is the probability of getting tails on both tosses?
4. What is the probability of getting heads on the second toss, given that the first toss was tails?
5. How many total outcomes would there be if you toss the coin four times?

Tip: The sum of probabilities of all possible outcomes in an experiment always equals 1.