Math Problem Statement

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

Solution

To find the probability of ACA \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 AA only: 0.25
  • The probability of ABA \cap B: 0.05
  • The probability of ACA \cap C: 0.10
  • The probability of ABCA \cap B \cap C: 0.15
  • The probability of CC only: 0.15
  • The probability of CBC \cap B: 0.10

So, the total probability of ACA \cup C is the sum of these probabilities:

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

Let's compute the sum:

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

Therefore, the probability of ACA \cup C is 0.800.80.

Would you like further details or have any questions?

Here are some additional questions related to this topic:

  1. What is the probability of ABA \cap B?
  2. What is the probability of BCB \cup C?
  3. How would you find the probability of ABCA \cap B \cap C?
  4. What is the probability of AA only (not including any intersections)?
  5. What is the probability of CC only (not including any intersections)?
  6. How would you calculate the probability of ACA \cap C without using the diagram?
  7. What is the probability of BB 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.

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Math Problem Analysis

Mathematical Concepts

Probability
Set Theory
Venn Diagrams

Formulas

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Theorems

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Suitable Grade Level

High School