Probability calculator
Calculate A or B, A and B, neither event and A given B. Choose independent, mutually exclusive or known-intersection events.
Enter P(A) and P(B) as percentages. Choose their relationship; supply P(A and B) when known instead of assuming independence.
Result
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How to use this calculator
Enter P(A) and P(B) as percentages. Choose their relationship; supply P(A and B) when known instead of assuming independence.
Formula and method
P(A∪B)=P(A)+P(B)−P(A∩B). Independent events have P(A∩B)=P(A)P(B); mutually exclusive events have zero intersection.
Worked example
For independent events with probabilities 50% and 40%, both occur with probability 20%, at least one with 70%, and neither with 30%.
Limits and interpretation
Mutually exclusive events require P(A)+P(B)≤100%. A known intersection must fit both probabilities. P(A given B) is undefined when P(B)=0 and is shown as —.
Frequently asked questions
How should I interpret the result?
For independent events with probabilities 50% and 40%, both occur with probability 20%, at least one with 70%, and neither with 30%.
What inputs and assumptions are required?
Mutually exclusive events require P(A)+P(B)≤100%. A known intersection must fit both probabilities. P(A given B) is undefined when P(B)=0 and is shown as —.