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Cheat sheet · Class 11 · CBSE · Commerce Mathematics

Probability cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

CBSE Class 11 · Mathematics

Cheat sheet

Chapter 14Probability

P(A or B) = P(A) + P(B) − P(A and B).

1. Sample Space & Events

  • Random experiment, outcome, sample space S.
  • Events: impossible (∅), sure (S), simple, compound.
  • Mutually exclusive: A ∩ B = ∅. Exhaustive: A ∪ B ∪ … = S.

2. Axiomatic Probability

0≤P(A)≤10 \le P(A) \le 1P(S)=1P(S) = 1P(A′)=1−P(A)P(A') = 1 - P(A)
P(A∪B)=P(A)+P(B)−P(A∩B)P(A\cup B) = P(A) + P(B) - P(A\cap B)
P(A)=n(A)n(S)P(A) = \dfrac{n(A)}{n(S)} (equally likely outcomes)

3. Examples

Two coins: S = {HH, HT, TH, TT}; P(at least one head) = 3/4.

Card from a deck: P(king or heart) = 4/52 + 13/52 − 1/52 = 16/52.

4. Key Points

  • P(A − B) = P(A) − P(A ∩ B).
  • Odds in favour: P(A) : P(A′).
  • Two dice: 36 outcomes.
  • Mutually exclusive ⇒ P(A ∩ B) = 0.

Remember: Sample space | axioms | addition rule

Probability: questions and notes

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