Choose the best answer to the following question. Explain your reasoning with one or more complete sentences.
Suppose you toss one coin three times in a row and get​ heads, tails, heads​ (HTH). If you are interested in the number of heads that​ appear, which one of the following sets of three tosses has a different outcome but corresponds to the same event as the first set of​ tosses?
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Part 1
Choose the correct answer below.
A.
​HHT, because it has two results of one kind and one result of the other.
B.
​THT, because it has the opposite results from HTH.
C.
​HHH, because getting heads is more important than getting tails.
D.
​HHH, because it has two heads just like HTH.
E.
​HHT, because it has the same number of heads and tails as HTH.
F.
​THT, because it has two results of one kind and one result of the other.

The key to solving this problem is understanding that the event being described is the **number of heads** that appear in a set of three coin tosses. In the original set of tosses, **HTH**, there are exactly **two heads**.

The correct answer should also involve two heads, regardless of the order of heads and tails.

- Option A: **HHT** has two heads and one tail, which matches the number of heads in HTH. This corresponds to the same event.
- Option B: **THT** also has two heads, so it may seem correct, but it’s focusing on the opposite results rather than the number of heads.
- Option C: **HHH** has three heads, which is not the same as HTH.
- Option D: **HHH** has three heads, so this is incorrect.
- Option E: **HHT** has the same number of heads and tails as HTH.
- Option F: **THT** has two heads, but the reasoning given is not focused on the number of heads.

Thus, the best answer is **E. HHT, because it has the same number of heads and tails as HTH**.

Would you like more details on the logic used in probability events?

Here are 5 related questions to further explore:

1. What is the probability of getting exactly two heads in three coin tosses?
2. How many different outcomes are possible when tossing a coin three times?
3. If you toss a coin three times, what is the probability of getting heads on the first and second toss?
4. What does it mean for two events to correspond to the same outcome in probability?
5. How can we use combinations to determine the number of ways to get two heads in three tosses?

**Tip:** Always break down a problem into simpler events and focus on the critical variables, like the number of heads in this case.

Suppose you toss one coin three times in a row and get heads, tails, heads (HTH). If you are interested in the number of heads that appear, which one of the following sets of three tosses has a different outcome but corresponds to the same event as the first set of tosses?
A. HHT, because it has two results of one kind and one result of the other.
B. THT, because it has the opposite results from HTH.
C. HHH, because getting heads is more important than getting tails.
D. HHH, because it has two heads just like HTH.
E. HHT, because it has the same number of heads and tails as HTH.
F. THT, because it has two results of one kind and one result of the other.

Explore how to determine the probability of getting two heads in three coin tosses. This problem covers basic probability concepts such as outcomes and matching events based on the number of heads, suitable for students in Grades 6-8.

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