Conditional Probability Calculator
Calculate P(A|B) = P(A and B) / P(B).
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Enter the joint probability P(A and B) and the marginal probability P(B). The calculator divides P(A and B) by P(B) to give you P(A|B), the probability of A given that B has occurred. Both values must be between 0 and 1, and the joint probability cannot exceed P(B).
About This Calculator
Conditional probability measures the likelihood of event A occurring given that event B has already occurred. The formula P(A|B) = P(A and B) / P(B) is fundamental to probability theory and is the building block for Bayes' theorem, Markov chains, and statistical inference.
Frequently Asked Questions
What is the difference between joint and conditional probability?
Joint probability P(A and B) is the chance both events happen together. Conditional probability P(A|B) is the chance of A happening given B is already known to have happened.
Can conditional probability be greater than 1?
No. Since P(A and B) cannot exceed P(B), the ratio is always between 0 and 1.
When are events independent?
Events A and B are independent when P(A|B) = P(A). Knowing B occurred does not change the probability of A.