Math Problem Statement

Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 2; and D: the numbers do not add to 9. Express the given event in symbolic form. HINT [See Example 5.] Either the numbers add to 9 or the red die shows a 1. how many elements

Solution

To solve this, let’s express the event in symbolic form and then find the number of elements (outcomes) in this event.

Step 1: Define Events Symbolically

We have:

  • Event AA: The red die shows a 1.
  • Event BB: The numbers add to 4.
  • Event CC: At least one of the numbers is 2.
  • Event DD: The numbers do not add to 9.

The event we are given is: "Either the numbers add to 9 or the red die shows a 1."

Step 2: Express the Event in Symbolic Form

This statement translates to: Bc∪AB^c \cup A This is because BcB^c represents that the sum does not equal

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Math Problem Analysis

Mathematical Concepts

Probability
Set Theory
Events in Probability

Formulas

Union of events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Complement of an event: P(A') = 1 - P(A)

Theorems

Addition Rule for Probability
Basic Set Theory Operations

Suitable Grade Level

Grades 9-11

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