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
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
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