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Probability Calculator

Use favorable/total outcomes for a single event or enter P(A) and P(B) for an explicitly independent two-event model. Results include formulas, odds, complements, and an outcome breakdown.

Single event

Favorable outcomes

Total possible outcomes

For equally likely outcomes, P(event) = favorable / total.

Two independent events

P(A) %

P(B) %

12%P(A and B)

58%P(A or B)

28%A but not B

42%Neither

Independent model: P(A∩B)=P(A)P(B) · P(A∪B)=P(A)+P(B)-P(A∩B)

Odds & repeated-trial evidence

Extend the basic event probability with complement, odds, at-least-one and exact-binomial checks for repeated independent trials.

Probability audit

Independent trials n

Exactly k successes

Display

Outcome	Probability	Formula

Use the tool above, then refresh this verification.

Verification uses the visible inputs and keeps the original tool workflow intact.

Analysis reproducibility & method-fit audit

Capture the current inputs, analysis settings and visible result as stable fingerprints, then flag structural method-fit issues that can be checked from the entered data. This complements the page’s existing mathematical audit; it does not prove distributional assumptions or causal validity.

Run the analysis above, then refresh this reproducibility audit.

Browser-local provenance evidence. Statistical assumptions still require subject-matter and study-design judgment.

Core describe → test → interpret workflows

Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.

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Two-event relationship explorer

Compare independent, mutually exclusive, or known-intersection models while keeping the primary calculator above intact.

Product depth

RelationshipP(A ∩ B) %

Uses the P(A) and P(B) values from the primary calculator.

Interpret statistical results in context

Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.

How to use this Probability Calculator

Use favorable/total outcomes for a single event or enter P(A) and P(B) for an explicitly independent two-event model. Results include formulas, odds, complements, and an outcome breakdown.

Practical guide and verification

Use the tool above first. These notes explain how to interpret, verify and bound the result without displacing the primary workflow.

Define the relationship between events

Two-event probability depends on whether events are independent, mutually exclusive, or represented by a known intersection. The same P(A) and P(B) can produce different unions and intersections under different relationships, so the relationship must be stated before the calculation is interpreted.

Union and intersection are different questions

P(A∪B) means A or B or both, while P(A∩B) means both occur. The general union rule subtracts the intersection once because outcomes in both events were counted in each marginal probability.

Common mistake

Mutually exclusive and independent are not synonyms. Mutually exclusive nonzero events cannot happen together, whereas independent events may happen together and one event does not change the probability of the other.

Conditional probability

P(A|B) restricts attention to outcomes where B occurred and equals P(A∩B)/P(B) when P(B) is positive. A conditional probability can differ substantially from P(A), which is exactly why independence needs to be checked rather than assumed.

Verification

Confirm that all probabilities remain between 0 and 1, the intersection does not exceed either marginal probability, and the union is at least as large as each marginal probability but no greater than 1. These bounds catch many impossible inputs immediately.