EVERYDAY MATH
Probability calculator
Calculate an equally likely event, a complement, a two-event union with its intersection, or a conditional probability using explicitly separated models.
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No regional currency, unit or language profile is applied. This choice does not convert values or change formulas, results, routes or legal guidance.
Select the model that matches your known information. Enter probabilities as decimals from 0 to 1.
Event probability
0.3 (30%)- Complement probability
- 0.7 (70%)
- Unfavourable outcomes
- 7
The count model assumes every outcome is equally likely. This calculator does not infer independence, unequal outcome weights, or missing intersections.
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Verification and calculation details
- Purpose
- Probability calculator
- Variables and units
- Use the labelled fields and units shown in the calculator. Results use those units unless a conversion is stated.
- Formula and method
- The exact formula and worked example are shown below. Deterministic formula executed locally in the browser.
- Assumptions
- Only entered values and stated assumptions are included. Local fees, rules and professional requirements are excluded unless explicitly shown.
- Engine version
- 1.0.0
- Production verification baseline
- Release 63 · source
998803f - Verification run
release-v63-2026-09-20- Last verified
- — Automated release checks passing
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How this calculator works
For equally likely outcomes, P(E)=n(E)/n(S). The complement is P(Eᶜ)=1−P(E). For two events, P(E∪F)=P(E)+P(F)−P(E∩F). Conditional probability is P(E|F)=P(E∩F)/P(F), where P(F)>0.
Variables and inputs
- Probability model
- Required numeric input. allowlisted selection: equally likely counts, complement, union or conditional probability.
- First count or probability
- Required numeric input. whole non-negative count in the count model; probability from 0 to 1 in explicit-probability models.
- Second count or probability
- Optional numeric input. positive whole total in the count model; probability from 0 to 1 when required.
- Intersection probability
- Optional numeric input. from 0 to 1; within the feasible bounds set by both event probabilities.
How to interpret the result
The calculator returns event probability and percentage, complement probability for count or complement models, union probability when two events and their intersection are supplied, conditional probability when an intersection and non-zero conditioning event are supplied. Read each output against the assumptions you entered, compare alternatives one variable at a time, and use the result as an estimate rather than a promise.
Common mistakes to avoid
- Mixing units or entering a rate as a decimal when the field requests a percentage.
- Rounding intermediate values instead of the final displayed result.
- Leaving out a cost, timing rule or local requirement listed in the assumptions below.
Practical uses
Use the probability calculator to check a real scenario, compare a changed assumption and explain the arithmetic before relying on a quote, specification or decision.
Worked example
For P(E)=0.4, P(F)=0.5 and P(E∩F)=0.2, the union is 0.4+0.5−0.2=0.7, or 70%. For P(E∩F)=0.2 and P(F)=0.5, P(E|F)=0.2/0.5=0.4, or 40%.
Assumptions and limitations
- count-based outcomes are equally likely and the sample space is complete
- explicit probabilities describe the same experiment and event definitions
- the supplied intersection belongs to both stated events
- conditional probability is evaluated only when the conditioning event can occur
- does not infer independence or mutually exclusive events
- does not assign equal probability to outcomes unless the count model is deliberately selected
- does not estimate probabilities from data or predict real-world outcomes
- displayed decimals are rounded after full-precision calculation
Important notes
Results are estimates based on the values entered. Confirm rates, prices, units and professional requirements that apply in your location. Review the Answer Atlas Calculation Standard and corrections policy for formula, privacy and correction rules.
Frequently asked questions
When can I divide favourable outcomes by total outcomes?
Only when the listed outcomes are equally likely and the total count describes the complete sample space.
Why does the union model need an intersection?
Outcomes in both events would otherwise be counted twice. Subtracting P(E∩F) once produces P(E∪F).
Why can conditional probability not divide by zero?
P(E|F) is defined as P(E∩F)/P(F). If P(F)=0, that expression is undefined, so the calculator rejects it.