Probability Calculator
Probability Formulas
Single Event
A and B (Independent)
A or B
Conditional
Common Probabilities
Related Calculators
Understanding Probability
What is Probability?
Probability measures how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). It can also be expressed as a percentage (0% to 100%) or as odds (like 3:1).
Basic Probability Formula
Types of Probability
Independent Events
Events that don't affect each other. The outcome of one doesn't change the probability of the other.
Dependent Events
Events where one outcome affects the other. Requires conditional probability.
Probability Rules
| Rule | Formula | Example |
|---|---|---|
| Complement | P(not A) = 1 - P(A) | P(not 6) = 5/6 |
| Addition (OR) | P(A or B) = P(A) + P(B) - P(A and B) | Either event occurs |
| Multiplication (AND) | P(A and B) = P(A) × P(B) | Both events occur |
| Conditional | P(B|A) = P(A and B) / P(A) | B given A occurred |
Converting Between Formats
Probability → Percentage
Probability → Odds
Odds → Probability
Common Misconception
The "Gambler's Fallacy" is the mistaken belief that past events affect future independent events. If you flip 5 heads in a row, the next flip is still 50/50 - the coin has no memory. Each flip is independent.
Frequently Asked Questions
What is the basic probability formula?
The basic probability formula is P(A) = favorable outcomes / total outcomes. For example, the probability of rolling a 6 on a fair die is 1/6 because there's 1 favorable outcome (rolling 6) out of 6 total possible outcomes.
How do you calculate the probability of two events both happening?
For independent events, multiply their probabilities: P(A and B) = P(A) × P(B). For example, the probability of flipping two heads in a row is 0.5 × 0.5 = 0.25. For dependent events, use conditional probability: P(A and B) = P(A) × P(B|A).
What is the difference between probability and odds?
Probability is the chance of success divided by all outcomes (successes + failures). Odds are the ratio of success to failure. If probability is 0.25 (25%), the odds are 1:3 (1 success for every 3 failures). To convert: odds = p/(1-p).
What is conditional probability?
Conditional probability P(B|A) is the probability of B occurring given that A has already occurred. It's calculated as P(B|A) = P(A and B) / P(A). For example, the probability of drawing a second ace given you already drew one ace from a deck.