Probability Calculator
Calculate event, complement, combined, and binomial probabilities.
How do I calculate probability?
A probability is the number of favourable outcomes divided by the number of possible outcomes, between zero and one.
Formula: P(event)=favorable÷total; P(not A)=1−P(A); independent P(A and B)=P(A)P(B); binomial P(X=k)=C(n,k)p^k(1−p)^(n−k).
Probability
0.166666666667
- Percentage
- 16.66666667%
- Odds against
- 5
What this calculator does
Find common probabilities from outcomes or decimal probabilities, including independent events and exact binomial results.
Use it to turn Calculation, Favorable outcomes, Total outcomes, Probability A / success, and the other shown inputs into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this math calculation.
Inputs and what they mean
- Calculation
- — choice value.
- Favorable outcomes
- — number value.
- Total outcomes
- — number value.
- Probability A / success
- — number value.
- Probability B
- — number value.
- Number of trials
- — number value.
- Exact successes
- — number value.
How to use it
- Enter the requested values.
- Choose the calculation mode when available.
- Review the result and supporting breakdown.
Formula
Methodology type: scientific equation.
Methodology: OpenStax introductory statistics, finite equally likely outcomes, complements, independent events and binomial probability.
Event counts assume equally likely outcomes. Joint modes require independence. Binomial mode requires independent equal-probability Bernoulli trials and supports up to 170 trials; no distribution is inferred from data.
P(event)=favorable÷total; P(not A)=1−P(A); independent P(A and B)=P(A)P(B); binomial P(X=k)=C(n,k)p^k(1−p)^(n−k).
Inputs used: Calculation, Favorable outcomes, Total outcomes, Probability A / success, Probability B, Number of trials, Exact successes.
Edge handling: Favorable outcomes is required.; Favorable outcomes cannot be negative.; Total outcomes is required.; Total outcomes must be greater than zero.; Probability A / success is required..
Worked example
Exactly 5 successes in 10 trials
- Start with Calculation: binomial, Favorable outcomes: 1, Total outcomes: 6, Probability A / success: 0.5, Probability B: 0.5, Number of trials: 10.
- Apply the method: P(event)=favorable÷total; P(not A)=1−P(A); independent P(A and B)=P(A)P(B); binomial P(X=k)=C(n,k)p^k(1−p)^(n−k).
- At p=0.5, the probability is 0.24609375.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Only the named probability models; assumptions must be justified externally.
- Binomial computation supports at most 170 trials; no inferred demand or medical risk model.
- For education and operational analysis only. No diagnosis, treatment recommendations, prescribing, dosing instructions, or reimbursement entitlement. Scientific calculations require appropriate laboratory verification; operational estimates do not replace local clinical, safety or financial policies.
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this probability calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: OpenStax
Last reviewed:
Common questions
How do I calculate probability?
A probability is the number of favourable outcomes divided by the number of possible outcomes, between zero and one. Check the formula, example, and limitations on this page before using the result for a real math decision.
What does independent mean?
One event does not change the probability of the other. Check the formula, example, and limitations on this page before using the result for a real math decision.
How should probabilities be entered?
Use decimals from 0 to 1, such as 0.25 for 25%. Check the formula, example, and limitations on this page before using the result for a real math decision.
Does binomial mode infer independence or success probability?
No. You supply success probability and must justify independent identical Bernoulli trials; the tool supports up to 170 trials.
How do I use the Probability Calculator?
Enter the required values for Calculation, Favorable outcomes, Total outcomes, Probability A / success, Probability B, and the other fields shown. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Probability Calculator use?
P(event)=favorable÷total; P(not A)=1−P(A); independent P(A and B)=P(A)P(B); binomial P(X=k)=C(n,k)p^k(1−p)^(n−k). The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Sources
Method based on OpenStax.
Cite this page
Free Calculator. (2026, October 23). Probability Calculator. https://freecalculator.tech/tools/probability-calculator
"Probability Calculator." Free Calculator, 23 Oct. 2026, https://freecalculator.tech/tools/probability-calculator.
Probability Calculator — Free Calculator, https://freecalculator.tech/tools/probability-calculator
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