Calculadora de Probabilidade Condicional
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
P(A|B) = P(A∩B) / P(B)
About this calculator
The Conditional Probability Calculator determines the chance of event A occurring given that event B has already occurred. The formula used is P(A|B) = P(A∩B) / P(B), where P(A∩B) is the probability of both events happening together and P(B) is the probability of the conditioning event. This tool is essential in fields such as statistics, data analysis, and decision-making under uncertainty.
To use the calculator, enter the values for P(A∩B) and P(B) as decimals between 0 and 1. The result will be the conditional probability P(A|B). For example, if the probability of rain and you leaving home is 0.3 and the probability of rain is 0.5, then the probability of you leaving home given it rained is 0.6. Remember that P(B) must be greater than zero.
Common use cases include medical diagnostics (probability of a disease given a symptom), risk analysis in finance (probability of default given an indicator), and quality testing (probability of defect given a process failure). The calculator helps update beliefs based on new information, a central concept in Bayesian inference.
Cautions: ensure the entered probabilities are consistent (P(A∩B) cannot be greater than P(B)). Also, conditional probability is not commutative: P(A|B) usually differs from P(B|A). The calculator assumes events are from the same sample space and that P(B) is known accurately.
Frequently asked questions
What does P(A|B) mean?
It is the probability of event A occurring given that event B has occurred. It reads 'probability of A given B'.
Can I use the calculator if P(B) is zero?
No. The formula requires P(B) to be greater than zero because division by zero is undefined.
What is the difference between P(A|B) and P(B|A)?
They are usually different. P(A|B) is the chance of A given B, while P(B|A) is the chance of B given A. The calculator only provides P(A|B).
How can I get P(A∩B) if I don't have that value?
If you have P(A) and P(B|A), you can compute P(A∩B) = P(A) * P(B|A). Otherwise, you need additional data or assumptions.
Does the calculator work for independent events?
Yes. If A and B are independent, P(A|B) = P(A). The calculator will return the same value as P(A∩B)/P(B), which equals P(A).