https://file.aiquickdraw.com/mathbot/file/1722874499621n9c52wim.jpg

Use the venn diagram to find the probability of A **∪** C.

To find the probability of \(A \cup C\) (the union of sets A and C), we need to sum the probabilities of all regions that fall within either set A, set C, or both. In the provided Venn diagram, these regions are:

- The probability of \(A\) only: 0.25
- The probability of \(A \cap B\): 0.05
- The probability of \(A \cap C\): 0.10
- The probability of \(A \cap B \cap C\): 0.15
- The probability of \(C\) only: 0.15
- The probability of \(C \cap B\): 0.10

So, the total probability of \(A \cup C\) is the sum of these probabilities:

\[ P(A \cup C) = 0.25 + 0.05 + 0.10 + 0.15 + 0.15 + 0.10 \]

Let's compute the sum:

\[ P(A \cup C) = 0.25 + 0.05 + 0.10 + 0.15 + 0.15 + 0.10 = 0.80 \]

Therefore, the probability of \(A \cup C\) is \(0.80\).

Would you like further details or have any questions?

Here are some additional questions related to this topic:
1. What is the probability of \(A \cap B\)?
2. What is the probability of \(B \cup C\)?
3. How would you find the probability of \(A \cap B \cap C\)?
4. What is the probability of \(A\) only (not including any intersections)?
5. What is the probability of \(C\) only (not including any intersections)?
6. How would you calculate the probability of \(A \cap C\) without using the diagram?
7. What is the probability of \(B\) only (not including any intersections)?
8. Can you explain the concept of mutually exclusive events using this Venn diagram?

**Tip:** When working with Venn diagrams, carefully identify each distinct region and ensure to include all relevant parts when calculating the union or intersection of sets.

Learn how to calculate the probability of the union of sets A and C using a Venn diagram. Step-by-step solution includes identifying regions and summing probabilities. Suitable for high school students and anyone interested in probability 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