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Probability Calculator

Calculate basic probabilities and conditional probabilities

P(A and B) - Provide P(A ∩ B) or choose an assumption

Provide the joint probability or choose an assumption below.

Independent events: P(A|B) = P(A) - occurrence of B doesn't affect A. Example: Two separate coin flips.

Mutually exclusive events: P(A ∩ B) = 0 - events cannot occur together. Example: Rolling a 2 or a 5 on a single die.

⚠️ Events cannot be both independent and mutually exclusive (unless one has probability 0).

Results

Enter values and click Calculate to see the result.

common.theory.probabilityCalculations

common.theory.probabilityMeasures

  • AND (Intersection): common.theory.andIntersectionRule
  • OR (Union): common.theory.orUnionRule
  • Conditional: common.theory.conditionalRule
  • Complement: common.theory.complementRule
  • Independent Events: common.theory.independentEventsRule
  • Mutually Exclusive: common.theory.mutuallyExclusiveRule

common.theory.understandingRulesHelps

\(P(A \cup B) = P(A) + P(B) - P(A \cap B), P(A|B) = \frac{P(A \cap B)}{P(B)}, P(A') = 1 - P(A)\)

Worked Examples

common.theory.example1

\(\text{Rolling a die: } P(\text{even}) = \frac{3}{6} = 0.5 \text{ or } 50\%\)

common.theory.example2

\(\text{Two coins: } P(\text{both heads}) = 0.5 \times 0.5 = 0.25 \text{ or } 25\%\)

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Probability Calculator | MathCalcLab | MathCalcLab