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Probability

General

Probability (Statistics)

A numeric measure, between 0 and 1, of how likely an event is to occur — with 0 meaning impossible and 1 meaning certain.

Definition

Probability is a numeric measure of how likely an event is to occur, expressed as a value between 0 (impossible) and 1 (certain) — or equivalently, as a percentage between 0% and 100%. It underlies everything from simple games of chance to complex statistical models used in science, finance, and quality control.

The Probability Calculator computes basic event probabilities, while the Binomial Distribution Calculator and Poisson Distribution Calculator extend probability to model repeated trials and rare events over an interval, respectively.

Formula

Basic Probability = Favorable Outcomes ÷ Total Possible Outcomes

For independent events A and B occurring together:

P(A and B) = P(A) × P(B)

Worked Example

The probability of drawing an ace from a standard 52-card deck is 4 ÷ 52 ≈ 7.7%, since there are 4 aces (favorable outcomes) among 52 total cards. Drawing two aces in a row, with replacement (so the deck resets between draws, keeping the events independent), has a probability of (4/52) × (4/52) ≈ 0.59%.

Key Things to Know

  • Probability always falls between 0 and 1: a value outside this range indicates a calculation error.
  • Independent events multiply: the probability of two independent events both occurring is the product of their individual probabilities.
  • The binomial distribution models fixed-trial counting: like the number of successes in a set number of coin flips or product tests.
  • The Poisson distribution models rate-based rare events: like the number of calls a call center receives per hour.
  • The normal distribution extends probability to continuous data, using area under a bell curve rather than counting discrete outcomes.

Related Calculators

Probability Calculator →Calculate the probability of any event. Enter favourable and total outcomes to find probability, percentage, complement, and odds in favour and against. Free online tool.
Binomial Distribution Calculator →Calculate binomial probability P(X = k) and cumulative P(X ≤ k) in seconds. Enter number of trials, probability of success, and number of successes to get results.
Poisson Distribution Calculator →Calculate Poisson probability P(X = k) for any event count in seconds. Enter the average rate (lambda) and number of events to get exact and cumulative probabilities.

Related Terms

Normal DistributionGaussian DistributionPercentilePercentile Rank

Frequently Asked Questions

Basic probability = Number of Favorable Outcomes ÷ Total Number of Possible Outcomes. For example, the probability of rolling a 4 on a fair six-sided die is 1 ÷ 6 ≈ 16.7%, since there's one favorable outcome out of six equally likely possibilities. The [Probability Calculator](/probability-calculator/) computes this ratio directly.
The binomial distribution models the number of successes across a fixed number of independent trials, each with the same success probability — like the number of heads in 20 coin flips. The Poisson distribution instead models the number of times a rare event occurs over a continuous interval (time, distance, area) when you know the average rate but not a fixed trial count — like customer arrivals per hour.
No — probability is always between 0 and 1 inclusive, where 0 means an event is impossible and 1 means it's certain. A calculated value outside this range signals an error in the underlying calculation, since it violates the basic definition of probability.
Two events are independent if the occurrence of one doesn't affect the probability of the other occurring — like two separate coin flips, where the result of the first flip has no bearing on the second. For independent events, the probability of both occurring is simply the product of their individual probabilities.
The normal distribution assigns probability across a continuous range of values using its bell-curve shape, where the area under the curve between two points represents the probability of a value falling in that range. This connects discrete probability concepts (like coin flips) to continuous data (like heights or test scores) through the same underlying framework.