Here are the solutions to the questions step by step:

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a) Find the sample space of the experiment.

The sample space is the set of all possible outcomes when a six-sided die is rolled. Each face of the die has a unique number of dots ranging from 1 to 6.

The sample space $S$ is: $S = \{1, 2, 3, 4, 5, 6\}$

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b) Find the event "an odd number is rolled".

Odd numbers on a six-sided die are $1, 3,$ and $5$.

The event $E_{\text{odd}}$ is: $E_{\text{odd}} = \{1, 3, 5\}$

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c) Find the event "a number less than 4 is rolled".

The numbers less than 4 on a six-sided die are $1, 2,$ and $3$.

The event $E_{\text{less than 4}}$ is: $E_{\text{less than 4}} = \{1, 2, 3\}$

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Would you like me to explain the reasoning further or provide additional examples? Let me know if you'd like to expand on this topic!

Related Questions:

1. How would the sample space change if a die with 8 sides is rolled?
2. What is the probability of rolling an even number on a six-sided die?
3. If two six-sided dice are rolled, what is the sample space of the experiment?
4. What is the probability of rolling a number greater than 4 on a single roll?
5. How do you find the complement of the event "an odd number is rolled"?

Tip:

When working with dice-related problems, visualizing the outcomes or writing them out in roster form can help organize your solution and make it clearer.