Conditional Probability Calculator
Conditional probability quantifies the probability of event A given that event B has occurred. This calculator uses two methods: the definition P(A|B) = P(A and B) / P(B), or Bayes theorem for computing posterior probabilities. Essential for understanding medical testing, decision-making with evidence, and updating beliefs with new information.
Conditional probability formulas
Definition: P(A|B) = P(A and B) / P(B)
Bayes Theorem: P(A|B) = P(B|A) * P(A) / P(B)
Key insight
- Conditional probability reflects how new information (B) changes our belief about A.
- Bayes theorem inverts conditional probabilities, useful for diagnosis and updating prior beliefs.
Conditional probability: frequently asked questions
What is conditional probability?
Conditional probability P(A|B) is the probability of event A occurring given that event B has occurred. It updates our probability based on new information.
What is Bayes theorem?
Bayes theorem: P(A|B) = P(B|A) * P(A) / P(B). It relates conditional probabilities in opposite directions, useful for updating beliefs with new evidence.
How do I calculate P(A|B) from definition?
P(A|B) = P(A and B) / P(B). The probability of both A and B divided by the probability of B.
When is conditional probability useful?
Medical testing (probability of disease given positive test), spam filtering (probability email is spam given certain words), and decision-making with new information.
Official sources
- NIST/SEMATECH e-Handbook: NIST Handbook.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.