STEMHub.tools
Probability · Events

Classical & Conditional Probability Calculator

Calculate classical probability, event unions, complements, conditional probability, and test independence from compatible event data.

Formula shown Runs locally Reviewed Aug 11, 2026
Follow us on Google
Equation guide

Events in a finite sample space or a probability model

Classical model

P(E)=favorable/total

Union

P(A∪B)=P(A)+P(B)−P(A∩B)

Conditional

P(A|B)=P(A∩B)/P(B)P(B)>0
Probability · Events

Model classical and conditional probability

Probabilities use values from 0 to 1. Classical mode requires whole outcome counts.

Inputs and displayed decimal results use at most three decimal places. Exact internal values are retained during calculation.

P(E) = favorable/total

Choose a model and enter compatible event data.

Using the model

Symbols, assumptions and limitations

Interpretation notes

Classical probability assumes equally likely outcomes. Event probabilities must lie from 0 to 1 and intersections must satisfy probability bounds. Conditional probability requires P(B)>0.

Worked examples

See the method in practice

01

Classical probability

Drawing one of 3 favorable objects from 10 equally likely objects gives probability 3/10 = 0.3.

02

Conditional probability

If P(A∩B)=0.2 and P(B)=0.4, then P(A|B)=0.5.

Questions

Frequently asked

What is a complement?

The complement contains all outcomes outside the event, so P(not E)=1−P(E).

When are events independent?

Events A and B are independent when P(A∩B)=P(A)P(B).

Why must intersection values be checked?

An intersection cannot exceed either event and cannot be smaller than the lower bound imposed by their union.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax Introductory Statistics — Probability Topics

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology