Conditional Probability Calculator
Calculate the probability of event A given that event B has occurred using the conditional probability formula.
P(A|B)
0.300000
P(A|B) vs P(A and B)
Formula
## How to Calculate Conditional Probability ### Formula **P(A|B) = P(A and B) / P(B)** Conditional probability measures how the probability of event A changes when we know event B has occurred. The vertical bar "|" is read as "given". P(B) must be greater than zero.
Exemplo Resolvido
P(A and B) = 0.12 and P(B) = 0.4. Find P(A|B).
- 01P(A|B) = P(A and B) / P(B)
- 02P(A|B) = 0.12 / 0.4
- 03P(A|B) = 0.3
- 04As a percentage: 30%
Perguntas Frequentes
What does conditional probability mean intuitively?
It restricts the sample space to only those outcomes where B occurred, then asks what fraction of those also have A. It updates our belief about A after learning B happened.
Is P(A|B) the same as P(B|A)?
No. P(A|B) and P(B|A) are generally different. They are related through Bayes' theorem: P(A|B) = P(B|A) * P(A) / P(B).
When are events independent in terms of conditional probability?
Events A and B are independent if P(A|B) = P(A), meaning knowing B occurred does not change the probability of A.
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