List the elements of the sample space defined by each experiment.

Roll a single die and then toss a coin.

{1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}{1HT, 2HT, 3HT, 4HT, 5HT, 6HT}     {HH, HT, TH, TT}{HH, HT, TH, TT, 1, 2, 3, 4, 5, 6}{1, 2, 3, 4, 5, 6, H, T}{1, 2, 3, 4, 5, 6}

When rolling a single die and then tossing a coin, the sample space includes all possible outcomes of the die roll followed by all possible outcomes of the coin toss. Each element of the sample space is a pair consisting of a number from the die (1 to 6) and a result from the coin toss (H or T).

The correct sample space for this experiment is:

**{1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}**

This set lists all possible outcomes where each die result is followed by either heads (H) or tails (T).

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What is the probability of rolling a 4 and getting heads?
2. How does the sample space change if you roll two dice and then toss a coin?
3. What is the probability of rolling an even number and getting tails?
4. If the die is biased towards 6, how would that affect the probabilities in the sample space?
5. Can you generalize the sample space for rolling an \(n\)-sided die and then tossing a coin?

**Tip:** In combined experiments, the sample space is created by considering all possible outcomes of each component event, leading to a larger set of possibilities.

Explore the concept of sample space in probability by rolling a single die and tossing a coin. Learn how to list all possible outcomes and calculate probabilities for specific events. Suitable for Grades 7-9.

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