Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 3; C: at least one of the numbers is 5; and D: the numbers do not add to 8. Express the given event in symbolic form.

We are given four events involving rolling two dice, one red and one green. Let's define these events symbolically based on the conditions provided:

- Event **A**: The red die shows a 4. 
  This can be written as \( A = \{ (4, y) \mid y \in \{1, 2, 3, 4, 5, 6\} \} \), where the red die is fixed at 4, and the green die takes any value from 1 to 6.

- Event **B**: The numbers add to 3. 
  This can be written as \( B = \{ (x, y) \mid x + y = 3 \} \). The possible pairs are \( (1, 2), (2, 1) \).

- Event **C**: At least one of the numbers is 5. 
  This can be written as \( C = \{ (x, y) \mid x = 5 \text{ or } y = 5 \} \). The possible pairs include all cases where either the red die or the green die is 5.

- Event **D**: The numbers do not add to 8.
  This can be written as \( D = \{ (x, y) \mid x + y \neq 8 \} \). This includes all outcomes except those where the sum is 8.

Would you like further details on how these sets are constructed or examples of specific elements in each? 

Here are 5 related questions to further explore:

1. What is the probability of event A occurring?
2. What are the possible outcomes of event C in a set notation?
3. How many outcomes are in event D?
4. Can events B and D occur simultaneously? Why or why not?
5. How do you find the intersection of events A and B?

**Tip**: When working with probability, always verify if events are mutually exclusive, meaning they cannot happen at the same time.

Understand how to express events in symbolic form when rolling two dice. This example problem includes key probability concepts and set notation: event A (red die shows 4), event B (numbers add to 3), event C (one number is 5), and event D (numbers do not add to 8). Suitable for high school students learning probability and set theory.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation