Conditional Probability Calculator
Find P(A given B) from the joint probability P(A ∩ B) and P(B).
Formula
P(A|B) = P(A ∩ B) / P(B), with 0 ≤ P(A ∩ B) ≤ P(B) and P(B)>0.
Conditional probability P(A|B) ≈ (0.2)÷(0.5) · Conditional probability (%) ≈ 100×(0.4)
How to use
- Enter the joint probability as a decimal.
- Enter the positive probability of B.
- Read P(A given B) as a decimal and percent.
Examples
- P(A ∩ B)=0.2 and P(B)=0.5 give P(A|B)=40%.
Frequently asked questions
What does given B mean?
B is known to have occurred, so the probability is assessed within B.
Can P(B) be zero?
No. This conditional-probability formula is undefined when P(B)=0.
Must the events be independent?
No. The intersection already captures their dependence; it cannot exceed P(B).
Sources
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