Probability calculator

Calculate A or B, A and B, neither event and A given B. Choose independent, mutually exclusive or known-intersection events.

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Set your data

Probability of A (%)

Probability of B (%)

Event relationship

Probability of A and B (%)

Enter P(A) and P(B) as percentages. Choose their relationship; supply P(A and B) when known instead of assuming independence.

Result

Enter your data and run the tool. Your result will appear here.

Probability and observed frequency

Simulate independent draws with replacement. A success is A or B, including when both occur. Each button starts a new sample.

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How to use the tool

Simulate independent draws with replacement. A success is A or B, including when both occur. Each button starts a new sample.

Fill in these fields: Probability of A (%), Probability of B (%), Event relationship.
Select “Calculate” to obtain the result.
Enter P(A) and P(B) as percentages.
Choose their relationship; supply P(A and B) when known instead of assuming independence.

Method and principles

Formula

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

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%.

Practical example

Input

Probability of A (%): 50
Probability of B (%): 40
Event relationship: Independent

Result

70%

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 —.

Example results (A 50%, B 40%)

Example results (A 50%, B 40%)
Parameter	Value
A or B · at least one	70%
A and B · intersection	20%
Neither A nor B	30%
A given B (— if B=0)	50%

Limits and checks

Limits and checks
Parameter	Value
Probability of A (%)	≥ 0; ≤ 100
Probability of B (%)	≥ 0; ≤ 100