# Probability Notes, Class 11 Mathematics | SwaVid Probability, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/probability Source: https://www.swavid.com/cbse/class-11/maths/chapter/probability # Probability ## Formulas and definitions ## Key ideas ## Common mistakes ## Quick checks ## Keep going ## Questions parents ask ## Class 11 Mathematics on SwaVid ### Random experiments and sample spaces ### Events and types of events ### Algebra of events ### Mutually exclusive and exhaustive events ### Axiomatic approach to probability ### Addition rule of probability ### Related chapter ### Related chapter ### All chapters SwaVid › CBSE › Class 11 › Mathematics › Probability Notes written by SwaVid from the NCERT textbook. Class 11 Mathematics, Chapter 14. Key ideas, formulas and common mistakes. CBSE does not print marks for a single chapter. Short answer. This chapter introduces the axiomatic approach to probability using set theory, sample spaces, and events. Students learn to calculate probabilities of events, including complementary, mutually exclusive, and exhaustive events using standard set operations. Source: NCERT Mathematics (Reprint 2026-27) , Chapter 14, Probability An experiment is called random if it has more than one possible outcome and the outcome cannot be predicted in advance. The set of all possible outcomes of a random experiment is called the sample space, denoted by S. Any subset of a sample space S is an event. An event consisting of a single sample point is an elementary or simple event, while an event containing more than one outcome is a compound event. The empty set represents an impossible event, and the entire sample space S represents a sure event. Events can be combined using set operations. The event 'A or B' corresponds to the union A ∪ B, 'A and B' corresponds to the intersection A ∩ B, and 'not A' corresponds to the complement A' or S - A. The event 'A but not B' is given by A - B = A ∩ B'. Two events A and B are mutually exclusive if they cannot occur at the same time, meaning A ∩ B = ∅. A set of events is exhaustive if their union equals the complete sample space S. Let S be a finite sample space. A real-valued function P assigns a probability P(ωᵢ) to each outcome such that 0 ≤ P(ωᵢ) ≤ 1 and the sum of probabilities of all elementary outcomes equals 1. For any event A, P(A) is the sum of probabilities of all outcomes in A. For any two events A and B, the probability of A ∪ B is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B). If A and B are mutually exclusive, then P(A ∪ B) = P(A) + P(B). Try each question first. Then tap it to see the answer. Sample space S = {HH, HT, TH, TT}, so n(S) = 4 Event A of getting at least one head = {HH, HT, TH}, so n(A) = 3 P(A) = n(A) / n(S) = 3 / 4 3 / 4 Since A and B are mutually exclusive, P(A ∩ B) = 0 P(A ∪ B) = P(A) + P(B) = 3 / 5 + 1 / 5 = 4 / 5 4 / 5 By de Morgan's law, A' ∩ B' = (A ∪ B)' P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.5 + 0.6 - 0.3 = 0.8 P(A' ∩ B') = 1 - P(A ∪ B) = 1 - 0.8 = 0.2 0.2 Sets . Permutations and Combinations . The 14 chapters of Class 11 Mathematics . The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment. No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed. This is the last chapter in the NCERT books for Class 11 Mathematics. SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works. - Ch 14 NCERT book - 80 marks, theory paper - 3 quick checks - Adding probabilities without subtracting the intersection for non-exclusive events . Check if events can happen simultaneously. If A and B share common outcomes, use P(A ∪ B) = P(A) + P(B) - P(A ∩ B) instead of just P(A) + P(B). - Confusing mutually exclusive events with exhaustive events . Mutually exclusive means the events have no overlap (A ∩ B = ∅). Exhaustive means together they cover the entire sample space (A ∪ B = S). - Writing P(A - B) as P(A) - P(B) . Subtract the probability of the intersection, not the entire event B. 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