Probability Calculator

Calculate various probability operations for events A and B

Probability Calculator

Calculate various probability operations for events A and B

Enter probabilities as decimals between 0 and 1 (e.g., 0.5 for 50%)

Formulas:

  • Union: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
  • Intersection: P(A ∩ B) = P(A) × P(B) (independent events)
  • Complement: P(A') = 1 - P(A)
  • Conditional: P(A|B) = P(A ∩ B) / P(B)
  • Bayes: P(B|A) = P(A|B) × P(B) / P(A)

About Probability Calculator

Our Probability Calculator helps you perform various probability operations including union, intersection, conditional probability, and Bayes theorem. These are fundamental concepts in probability theory and statistics.

Probability Operations:

Union (A ∪ B)

Probability that either event A or event B occurs (or both).

Formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Intersection (A ∩ B)

Probability that both event A and event B occur simultaneously.

Formula: P(A ∩ B) = P(A) × P(B) (for independent events)

Complement (A')

Probability that event A does not occur.

Formula: P(A') = 1 - P(A)

Conditional Probability (A|B)

Probability of event A occurring given that event B has occurred.

Formula: P(A|B) = P(A ∩ B) / P(B)

Bayes Theorem (B|A)

Updates the probability of event B based on new information about event A.

Formula: P(B|A) = P(A|B) × P(B) / P(A)

Applications:

  • Risk Assessment: Calculating probabilities of various outcomes
  • Medical Diagnosis: Using Bayes theorem for disease probability
  • Quality Control: Determining defect probabilities
  • Financial Modeling: Risk analysis and portfolio management
  • Machine Learning: Bayesian inference and classification