A random experiment consist of tossing a fair coin two time. What is the sample space?




Question 6Answer

a.

{HH, TT, HT, HT}




b.

{HH, HT, TH, TT}




c.

{HH, HT, TT}




d.

{HT, TH}

When you toss a fair coin two times, each toss has two possible outcomes: heads (H) or tails (T). The sample space includes all possible combinations of outcomes for the two tosses.

### Possible Outcomes:
1. First toss: Heads (H), Second toss: Heads (H) — Result: HH
2. First toss: Heads (H), Second toss: Tails (T) — Result: HT
3. First toss: Tails (T), Second toss: Heads (H) — Result: TH
4. First toss: Tails (T), Second toss: Tails (T) — Result: TT

### Sample Space:
\[
\text{Sample Space} = \{HH, HT, TH, TT\}
\]

### Answer:
The correct answer is **b. \{HH, HT, TH, TT\}**.

Would you like more details or have any other questions?

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Here are some related questions you might find interesting:
1. What is the probability of getting exactly one head when tossing a coin twice?
2. How does the sample space change if a coin is tossed three times instead of two?
3. What is the probability of getting at least one tail when tossing a coin twice?
4. How does the fairness of the coin affect the sample space?
5. What is the difference between sample space and an event?
6. Can you list all possible outcomes when a die is rolled twice?
7. How do you calculate the probability of multiple independent events occurring?
8. What are the different types of sample spaces (discrete, continuous)?

**Tip:** Always ensure you list all possible outcomes in a sample space to avoid missing any potential event!

Explore the concept of sample space in probability by analyzing the outcomes of tossing a fair coin twice. Learn about all possible combinations of heads (H) and tails (T) in this mathematical problem. Suitable for Grades 7-9.

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