Suppose two dice (one red, one green) are rolled. Consider the following events. *A*: the red die shows 3; *B*: the numbers add to 5; *C*: at least one of the numbers is 3; and *D*: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]

At least one of the numbers is 3, or the numbers add up to 5.

Let's denote the events based on the problem:

- **Event A**: The red die shows 3.
- **Event B**: The numbers add to 5.
- **Event C**: At least one of the numbers is 3.
- **Event D**: The numbers do not add to 10.

The problem asks us to express the event "At least one of the numbers is 3, or the numbers add up to 5" in symbolic form.

Based on the definitions provided:

- **Event C** represents "at least one of the numbers is 3."
- **Event B** represents "the numbers add to 5."

The word "or" in probability corresponds to the union of two events. So, the event "At least one of the numbers is 3, or the numbers add up to 5" can be expressed as the union of Events C and B:

\[
C \cup B
\]

### Final Answer:
The event "At least one of the numbers is 3, or the numbers add up to 5" is represented by the symbol **\( C \cup B \)**.

Would you like more details on how these events are calculated, or do you have any other questions?

Here are 5 related questions to consider:
1. What is the probability of Event C occurring?
2. What is the probability of Event B occurring?
3. How would you compute the probability of the union of two events, such as \( C \cup B \)?
4. What is the probability of both events C and B occurring simultaneously?
5. How does the event D relate to events B and C?

**Tip:** Understanding how to compute probabilities involving unions and intersections of events is crucial for solving more complex probability problems!

Suppose two dice (one red, one green) are rolled. Consider the following events. *A*: the red die shows 3; *B*: the numbers add to 5; *C*: at least one of the numbers is 3; and *D*: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.] At least one of the numbers is 3, or the numbers add up to 5.

Learn how to express and solve a probability problem involving two dice rolls, where one die shows 3 or the numbers add to 5. This problem explores set theory concepts, the union of events, and the addition rule for probability. Suitable for Grades 9-12.

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