Math Problem Statement
Given that P(A or B) = , P(A) = , and P(A and B) = , find P(B). Express the probability as a simplified fraction.
Solution
To find , we can use the formula for the probability of the union of two events and :
Given:
We can rearrange this formula to solve for :
Plug in the values once provided, and then simplify the result.
Please provide the values for , , and so we can continue.
Would you like more details about this process?
Here are 5 related questions:
- How is the union of probabilities different from their intersection?
- Why do we subtract when calculating ?
- How do we interpret probabilities as fractions in real-world scenarios?
- Can probabilities be greater than 1?
- What is the significance of mutually exclusive events in probability?
Tip: Always ensure probability values are between 0 and 1.
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Math Problem Analysis
Mathematical Concepts
Probability
Set Theory
Formulas
P(A or B) = P(A) + P(B) - P(A and B)
Theorems
Addition Rule for Probability
Suitable Grade Level
Grades 9-12