Free Probability Calculator for Simple Events, Independent AND/OR, Conditional Probability, Binomial Outcomes, and Odds

Calculate simple event probability, combine independent events with AND or OR, evaluate conditional probability from intersection and condition probabilities, or find an exact binomial outcome.

Browser-basedNo sign-upPrivate local historyStep-by-step

Interactive calculator

Mode

Value A / favorable / n

Value B / total / k

Probability p / intersection

Probability—

Percentage—

Complement—

Choose a mode and enter values.

How to use it

Choose the probability mode.
Enter counts for simple probability or decimal probabilities from 0 to 1 for event modes.
For binomial mode, enter n trials, k successes, and success probability p.
Calculate and review the complement and odds view.
Only use independent-event formulas when independence is a reasonable assumption.

What this calculator includes

1. Simple probabilityCompute favorable outcomes divided by total outcomes.

2. ComplementShow 1−P(A).

3. Independent ANDMultiply P(A) and P(B).

4. Independent ORUse P(A)+P(B)−P(A)P(B).

5. Conditional probabilityCalculate P(A∩B)/P(B).

6. Binomial exact kCompute C(n,k)p^k(1−p)^(n−k).

7. Odds in favorConvert probability to p:(1−p).

8. Percent outputShow probability as a percentage.

9. Input validationRequire probabilities from 0 through 1.

10. Formula stepsShow the selected probability identity.

11. Local historySave recent probability calculations.

12. Copy/downloadExport results and steps.

Result checklist

0 / 5 complete

Inputs use the intended units or interpretation.The formula mode matches the problem.The result magnitude is reasonable.I reviewed the shown calculation steps.I will round only at the final step.

Local calculation history

Formula and reference table

Case	Formula	Assumption
Simple	favorable / total	equally weighted outcomes if using counts
Independent AND	P(A)P(B)	A and B independent
Independent OR	P(A)+P(B)−P(A)P(B)	A and B independent
Conditional	P(A∩B)/P(B)	P(B)>0
Binomial exact	C(n,k)p^k(1−p)^(n−k)	fixed n, independent equal-p trials

Quick knowledge check

For independent events with P(A)=0.5 and P(B)=0.4, what is P(A and B)?

Related calculators

Permutation Calculator Statistics Calculator Percentile Calculator

Frequently asked questions

What is probability?

Probability is a number from 0 to 1 that quantifies the chance of an event under a specified model.

How do independent AND probabilities combine?

Multiply the probabilities: P(A∩B)=P(A)P(B) when the events are independent.

How do independent OR probabilities combine?

Add the probabilities and subtract their overlap; under independence the overlap is P(A)P(B).

What is conditional probability?

P(A|B) is the probability of A given B, calculated as P(A∩B)/P(B) when P(B)>0.

When is the binomial formula appropriate?

Use it for a fixed number of independent trials with the same success probability and a binary success/failure outcome.

Does the probability calculator run locally?

Yes. The interactive calculation runs in your browser and recent calculation history is stored locally in the browser.

Can I copy or download the result?

Yes. Use the copy and download controls to save the current result and calculation steps.

Scope and accuracy

Probability results are only as valid as the assumptions and inputs. Independence, equal outcome likelihood, and binomial trial assumptions must be justified by the real problem rather than inferred by the calculator.