Developing math vocabulary

Probability

Pronunciation: prob-uh-BIL-uh-tee

Probability measures how likely an event is, from 0 for impossible to 1 for certain.

Symbols and notationP(A)
Subject
Grade bands
Difficulty

Developing

Profession trailScientists & Astronomers

Plain language

What it means

Probability measures how likely an event is, from 0 for impossible to 1 for certain.

Formal meaning

Mathematical definition

For equally likely outcomes, P(A) = favorable outcomes/total outcomes; more generally, probability is a measure satisfying nonnegativity, normalization, and additivity.

Where it fits

Its place in mathematics

Probability supports risk, statistics, games, forecasting, reliability, genetics, finance, and scientific inference.

Why it matters

The practical reason to learn it

It turns uncertainty into quantities that can be compared, modeled, and tested.

−2−1012
From impossible to certainProbabilities can be written as fractions, decimals, or percentages between 0 and 1 inclusive.

Worked example

Find a simple probability

A fair six-sided die is rolled. What is the probability of an even result?

  1. List favorable outcomes: 2, 4, 6.
  2. Divide 3 favorable outcomes by 6 total outcomes.
Answer

The probability is 1/2, 0.5, or 50%.

Real-life example

Where this appears

A meteorologist communicates forecast uncertainty using probabilities based on models and observations.

Common mistake

What to watch for

Treating unlikely as impossible or adding probabilities for events that overlap without correcting the overlap.

Memory tip

Keep this in mind

Define the event and sample space before calculating.

Little-known fact

Keep curiosity alive

A probability of 0 can describe an event that is possible in a continuous model but occupies no interval of positive width.

A profession that uses this idea

Forecasts quantify uncertainty

Scientists use probability to express uncertainty, evaluate evidence, and compare possible outcomes.

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Prerequisites, related ideas and next concepts

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Related terms

People behind the ideas

Related Math Heroes

Blaise Pascal

Blaise Pascal was mathematician, physicist, and inventor. He worked on projective geometry, probability, fluid pressure, and a mechanical calculating machine.

Pierre de Fermat

Pierre de Fermat was lawyer and mathematician. He made major contributions to number theory, analytic geometry, probability, and methods for maxima and tangents.

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