Probability
Uttar Pradesh Board · Class 11 · Mathematics
Quick revision notes for Probability — Uttar Pradesh Board Class 11 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Events and Sample Space
- An event is any subset of a sample space S
- Sample space S contains all possible outcomes of an experiment
- Events can be classified as impossible, sure, simple, or compound
Types of Events and Event Operations
- Complementary event A' represents 'not A' and equals S - A
- Union A ∪ B represents 'A or B' - occurrence of at least one event
- Intersection A ∩ B represents 'A and B' - occurrence of both events
Axiomatic Approach to Probability
- Probability is a real-valued function P with domain as power set of S and range [0, 1]
- Three fundamental axioms define probability: non-negativity, normalization, and additivity
- For equally likely outcomes, P(ωᵢ) = 1/n where n is total number of outcomes
Probability Rules and Formulas
- Addition rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
- For mutually exclusive events: P(A ∪ B) = P(A) + P(B)
- Complement rule: P(A') = 1 - P(A)
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Probability covers several key topics that are frequently asked in Uttar Pradesh Board Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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