Math Problem Statement
Use the venn diagram to find the probability of A ∪ C.
Solution
To find the probability of (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 only: 0.25
- The probability of : 0.05
- The probability of : 0.10
- The probability of : 0.15
- The probability of only: 0.15
- The probability of : 0.10
So, the total probability of is the sum of these probabilities:
Let's compute the sum:
Therefore, the probability of is .
Would you like further details or have any questions?
Here are some additional questions related to this topic:
- What is the probability of ?
- What is the probability of ?
- How would you find the probability of ?
- What is the probability of only (not including any intersections)?
- What is the probability of only (not including any intersections)?
- How would you calculate the probability of without using the diagram?
- What is the probability of only (not including any intersections)?
- 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
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