Probability Calculator

Calculate probability of events

Common Probability Examples
Dice & Coins
  • Fair coin (heads): 1/2 = 0.5
  • Six-sided die (any number): 1/6 ≈ 0.167
  • Rolling a 6: 1/6 ≈ 0.167
  • Rolling even number: 3/6 = 0.5
Card Games
  • Drawing an Ace: 4/52 ≈ 0.077
  • Drawing a Heart: 13/52 = 0.25
  • Drawing a Face Card: 12/52 ≈ 0.231
  • Drawing a Red Card: 26/52 = 0.5

How the Probability Calculator Works

Our probability calculator provides three modes for computing different types of probability problems. The Basic Probability mode calculates the likelihood of a single event by dividing favorable outcomes by total possible outcomes. The Conditional Probability mode computes P(A|B) — the probability of event A occurring given that event B has already happened. The Multiple Events mode handles compound probability for two events, including both "and" (intersection) and "or" (union) calculations.

Each calculation mode displays results as a decimal, percentage, fraction, and odds format, giving you flexibility for any context — whether you are solving homework problems, analyzing data, or making informed decisions.

Probability Formula

P(A) = Favorable Outcomes / Total Outcomes

This fundamental formula underpins all probability calculations. For compound events, the rules expand: P(A and B) = P(A) × P(B) for independent events, and P(A or B) = P(A) + P(B) − P(A and B) for the union of two events. Conditional probability uses Bayes' theorem: P(A|B) = P(A ∩ B) / P(B). Understanding these formulas lets you solve problems ranging from simple coin flips to complex statistical analyses.

The complement rule is also essential: P(not A) = 1 − P(A). This is especially useful when it is easier to calculate the probability of an event not happening. For instance, the probability of rolling at least one six in four dice rolls is 1 − (5/6)⁴ ≈ 51.8%.

Frequently Asked Questions

Probability is a branch of mathematics that measures 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. Probability can also be expressed as a percentage (0% to 100%). The basic formula is P(A) = Number of Favorable Outcomes / Total Number of Possible Outcomes.

For two independent events A and B, the probability of both occurring is P(A and B) = P(A) × P(B). For the probability of either event occurring, use P(A or B) = P(A) + P(B) − P(A and B). For example, the probability of rolling a 3 on a die (1/6) AND flipping heads on a coin (1/2) is 1/6 × 1/2 = 1/12 ≈ 8.33%.

Conditional probability is the probability of an event occurring given that another event has already happened. It is written as P(A|B), read as "the probability of A given B." The formula is P(A|B) = P(A ∩ B) / P(B). For example, the probability of drawing a king from a deck given that a face card was drawn is P(King|Face Card) = (4/52) / (12/52) = 4/12 = 1/3.

Probability is used extensively in everyday life and professional fields. Weather forecasting uses probability to predict rain chances. Insurance companies calculate risk probabilities to set premiums. Medical researchers use probability in clinical trials. Sports analysts predict game outcomes. Financial analysts assess investment risks. Even simple decisions like carrying an umbrella involve informal probability assessment.

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