Math Problem Statement

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.

Solution

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:

CBC \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 CBC \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 CBC \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!

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Math Problem Analysis

Mathematical Concepts

Probability
Set Theory
Union of Events

Formulas

Union of events formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Theorems

Addition Rule for Probability

Suitable Grade Level

Grades 9-12