📚 Key Concepts
Conditional Probability- P(A|B) = P(A∩B)/P(B)
- Updating probability given new information
- Dependent vs Independent events
Multiplication Theorem- P(A∩B) = P(A) × P(B|A)
- For independent events: P(A∩B) = P(A) × P(B)
Independent Events- P(A|B) = P(A)
- P(B|A) = P(B)
- No influence on each other
🎯 Key Formulas
Bayes' Theorem:- P(A|B) = [P(B|A) × P(A)]/P(B)
- P(B) = P(B|A)P(A) + P(B|A')P(A')
Addition Rule:- P(A∪B) = P(A) + P(B) - P(A∩B)
Probability Tree:- Multiply along branches
- Add for different paths
⚠️ Common Mistakes to Avoid
Confusing independent/dependent eventsWrong application of Bayes' theoremIncorrect probability tree constructionMissing mutually exclusive conceptWrong multiplication rule usageForgetting to check for independence
📖 Knowledge Prerequisites
Basic probability conceptsSet theoryFractions and decimalsTree diagramsLogical reasoning
💡 Tips for Students
Draw probability treesCheck for independenceWrite sample space clearlyUse systematic approachVerify probabilities sum to 1Use real-world examples
👉 Practice Recommedations
Conditional probability problemsIndependence testingBayes' theorem applicationsTree diagram questionsReal-world scenariosMultiple event problemsMedical diagnosis problemsQuality control applications
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