Probability Calculators
Work out the likelihood of events, combine probabilities, and update beliefs with new evidence.
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). The calculators in this category cover the everyday questions that come up in coursework, risk assessment, and decision-making: what is the chance of A and B together, what is the chance of A given that B has happened, and how should a prior belief change after new evidence arrives.
Several tools here share the same underlying rules. Conditional probability, joint probability, and Bayes' theorem are three views of one relationship, so it helps to start with the concept and then choose the calculator that matches the numbers you already have.
Calculators in this category
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- ProbabilityBayes' Theorem CalculatorAvailable
- ProbabilityChebyshev's Theorem CalculatorAvailable
- ProbabilityConditional Probability CalculatorAvailable
- ProbabilityExpected Value CalculatorAvailable
- ProbabilityImplied Probability CalculatorAvailable
- ProbabilityJoint Probability CalculatorComing soon
- ProbabilityOdds CalculatorComing soon
- ProbabilityP-Hat CalculatorComing soon
- ProbabilityPost-Test Probability CalculatorComing soon
- ProbabilityProbability CalculatorComing soon
- ProbabilityProbability of 3 Events CalculatorComing soon
- ProbabilityRelative Risk CalculatorComing soon
- ProbabilityRisk CalculatorComing soon
Key concepts
- Sample space and event
- The sample space is the set of all possible outcomes. An event is any subset of it, and its probability is the total probability of the outcomes it contains.
- Conditional probability
- The probability of A given that B has occurred, written P(A|B). It restricts attention to the outcomes where B is true.
- Independence
- Two events are independent when knowing one occurred does not change the probability of the other, so P(A and B) = P(A) × P(B).
- Odds and probability
- Odds compare the chance an event happens to the chance it does not. The two are different scales for the same information and can be converted into each other.
Frequently asked questions
What is the difference between probability and odds?
Probability is the chance an event happens divided by all possible outcomes, so it always lies between 0 and 1. Odds are the ratio of the chance the event happens to the chance it does not. An event with probability 0.25 has odds of 1 to 3 in favour.
When can I multiply probabilities together?
Multiplying P(A) by P(B) gives the probability of both happening only when the events are independent. If the events influence each other, you need the conditional probability of one given the other instead.