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Probability Calculator

Quickly calculate the probability of simple and compound events.

Event A

Event B

Probability of Single Events

P(A)

P(Not A)

P(B)

P(Not B)

Probability of Compound Events

P(A and B)

P(A or B)

Note: Calculations for compound events (A and B, A or B) assume that Event A and Event B are independent.

Why Use This Tool? ✅

Accurate & Fast

Get precise probability values in decimal, fraction, and percentage formats instantly.

Supports Multiple Scenarios

Calculates simple, complementary, and compound probabilities for independent events.

Ideal for Learning

A great tool for students to check homework, explore concepts, and build intuition.

For Professional Use

Useful for analysts, data scientists, and anyone needing quick probability calculations.

The Science of Chance: A Guide to Probability 🎲

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. A probability is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.

Simple Probability: P(A)

The most basic form of probability involves a single event. It is calculated by dividing the number of ways the event can happen (favorable outcomes) by the total number of possible outcomes.

Formula: P(A) = Favorable Outcomes / Total Outcomes

Example: The probability of rolling a 4 on a standard six-sided die is 1 / 6, because there is one "4" (favorable outcome) and six total possible outcomes.

Complementary Probability: P(Not A)

The complement of an event A is the event that A does not occur, written as P(A') or P(Not A). The sum of the probability of an event and its complement is always 1.

Formula: P(Not A) = 1 - P(A)

Example: The probability of not rolling a 4 is 1 - (1/6) = 5/6.

Compound Probability for Independent Events

This tool also calculates probabilities for two independent events—where the outcome of one event does not affect the outcome of the other. Rolling two dice is a classic example.

  • The "AND" Rule (Intersection): The probability that both Event A and Event B occur is found by multiplying their individual probabilities.
    P(A and B) = P(A) × P(B)
  • The "OR" Rule (Union): The probability that either Event A or Event B (or both) occur is found by adding their probabilities and subtracting the probability of both occurring.
    P(A or B) = P(A) + P(B) - P(A and B)

This calculator handles all these scenarios, providing a comprehensive yet easy-to-use tool for exploring the world of probability.