What is probability?

Probability is a branch of mathematics that quantifies how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means it is certain. The classical definition, attributed to Pierre-Simon Laplace, states that the probability of an event equals the number of favorable outcomes divided by the total number of equally likely outcomes: $P(A) = \frac{\text{favorable outcomes}}{\text{total outcomes}}$.

Probability is foundational to statistics, data science, risk analysis, game theory, and everyday decision-making. Whether you're estimating the chance of rolling a six on a die, predicting weather outcomes, or evaluating the likelihood of a medical test result, probability provides the mathematical framework for reasoning about uncertainty.

Tool description

This probability calculator computes the probability of a single event using the classical formula. Enter the number of favorable outcomes and the total number of possible outcomes, and it instantly displays the result as a decimal, a percentage, and the full formula. The tool validates your inputs and provides clear error messages if the values are invalid.

How it works

The calculator divides the number of favorable outcomes by the total number of outcomes to produce a probability value between 0 and 1. It then converts that decimal to a percentage and renders the complete formula. Input validation ensures the total is not zero, neither value is negative, and the favorable count does not exceed the total.

$$P(A) = \frac{\text{favorable outcomes}}{\text{total outcomes}}$$

Features

  • Calculates probability as a decimal and a percentage
  • Displays the full probability formula with your values substituted in
  • Validates inputs: prevents division by zero, negative numbers, and favorable outcomes exceeding total outcomes
  • Handles very small probabilities with scientific notation for precision
  • Updates results instantly as you type

Use cases

  • Students solving probability homework problems and verifying their manual calculations
  • Quick probability checks for games, lotteries, or statistical experiments