Conditional Probability Calculator
Calculate P(A|B) using the definition P(A∩B)/P(B) with step-by-step explanation.
Inputs
P(A|B)
0.300000
Step by step
Values used
P(A ∩ B) = 0.1200; P(B) = 0.4000
Formula applied
P(A|B) = P(A ∩ B) / P(B)
P(A|B)
= 0.300000
How it works
Conditional probability P(A|B) is the probability of event A occurring given that event B has already occurred. It is defined as the ratio of the joint probability P(A∩B) to the marginal probability P(B).
Formula
P(A|B) = P(A ∩ B) / P(B)
- P(A∩B)
- Joint probability of A and B
- P(B)
- Probability of B (must be > 0)
Frequently Asked Questions
When is P(A|B) = P(A)?
When A and B are independent events — knowing B occurred does not change the probability of A.
Is P(A|B) the same as P(B|A)?
No. P(A|B) = P(A∩B)/P(B) while P(B|A) = P(A∩B)/P(A). They are related by Bayes' theorem.