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Let’s analyze each event and determine which outcomes correspond to them. Since there are 8 possible outcomes for three coin tosses, each outcome has a probability of \( \frac{1}{8} \).

### Outcomes:
The possible outcomes are:
1. TTT
2. HHT
3. HTT
4. TTH
5. HTH
6. HHH
7. THH
8. THT

### Event Analysis:

#### Event A: Exactly one head
Outcomes with exactly one head:
- HTT
- THT
- TTH

So, the outcomes for Event A are **HTT, THT, and TTH**.

Probability of Event A: \( \frac{3}{8} \).

#### Event B: More heads than tails
Outcomes with more heads than tails (i.e., at least two heads):
- HHT
- HTH
- HHH
- THH

So, the outcomes for Event B are **HHT, HTH, HHH, and THH**.

Probability of Event B: \( \frac{4}{8} = \frac{1}{2} \).

#### Event C: A head on each of the last two tosses
Outcomes with heads on the last two tosses:
- HHT
- HHH
- THH

So, the outcomes for Event C are **HHT, HHH, and THH**.

Probability of Event C: \( \frac{3}{8} \).

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### Summary Table:

| Event        | Outcomes                           | Probability |
|--------------|------------------------------------|-------------|
| Event A      | HTT, THT, TTH                      | \( \frac{3}{8} \) |
| Event B      | HHT, HTH, HHH, THH                 | \( \frac{1}{2} \) |
| Event C      | HHT, HHH, THH                      | \( \frac{3}{8} \) |

Would you like further details on any part of this solution? 

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Here are 5 additional questions to deepen your understanding:
1. How would the probabilities change if the coin was biased?
2. What would be the probability of getting exactly two heads in three tosses?
3. How many possible outcomes would there be if the coin was tossed four times?
4. Can you list all outcomes for an event with "at least one head" in three tosses?
5. How does increasing the number of coin tosses affect the number of possible outcomes?

**Tip:** When dealing with probabilities, remember that each unique outcome must be accounted for based on its individual conditions to ensure accuracy in your calculations.

A coin is tossed three times. An outcome is represented by a string like HTT. Analyze each of the three events: A (exactly one head), B (more heads than tails), and C (a head on each of the last two tosses) and determine the probability of each event.

Determine the probability of specific events when a coin is tossed three times. This example problem explores outcomes with exactly one head, more heads than tails, and heads on the last two tosses. Perfect for middle school students learning basic probability concepts.

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