Probability Calculator

Calculate basic, conditional, and Bayesian probability with visual aids and step-by-step solutions.

Loading...
1. Select the probability type you want to calculate - basic, conditional, or Bayesian. 2. For basic probability, enter the number of favorable outcomes and the total number of outcomes. 3. For conditional probability, provide P(A and B) and P(B) to compute P(A given B). 4. For Bayesian probability, enter the prior probability, likelihood, and evidence to compute the posterior. 5. Review the step-by-step solution and visual representation of the probability calculation.

About This Tool

Probability is the mathematical framework for reasoning about uncertainty, and it underpins everything from weather forecasts and medical diagnoses to game theory and machine learning. This calculator covers three essential types of probability calculations: basic probability of single and combined events, conditional probability (the chance of an event given that another has occurred), and Bayesian probability (updating beliefs based on new evidence).

For basic probability, enter the number of favorable outcomes and total outcomes to find the probability, or work with combined events using the addition and multiplication rules. The conditional probability section lets you compute P(A|B) when you know P(A and B) and P(B), which is critical for understanding dependent events. The Bayesian calculator applies Bayes' theorem to compute posterior probabilities from prior probabilities and likelihoods - one of the most powerful tools in statistics and data science.

Each calculation includes a step-by-step explanation and visual representation so you can understand not just the answer but the reasoning behind it. Whether you are a student learning probability for the first time, a professional making data-driven decisions, or someone trying to evaluate risks and outcomes, this tool makes probability accessible and intuitive.

Formula / How It Works

P(A) = favorable / total | P(A|B) = P(A and B) / P(B) | Bayes: P(H|E) = P(E|H) x P(H) / P(E)

Frequently Asked Questions

Basic probability calculates the likelihood of an event without additional information: P(A) = favorable outcomes / total outcomes. Conditional probability calculates the likelihood of an event given that another event has already occurred: P(A|B) = P(A and B) / P(B). Conditional probability is always relative to the reduced sample space defined by the given condition.
Bayes' theorem calculates the probability of a hypothesis given observed evidence. The formula is P(H|E) = P(E|H) x P(H) / P(E). It is used when you have a prior belief about something and want to update that belief after seeing new data. Common applications include medical testing, spam filtering, and risk assessment.
For independent events, multiply their individual probabilities: P(A and B) = P(A) x P(B). For dependent events, use P(A and B) = P(A) x P(B|A). Two coin flips are independent (1/2 x 1/2 = 1/4), while drawing two cards without replacement are dependent because the first draw changes the remaining deck.
The addition rule calculates the probability that at least one of two events occurs: P(A or B) = P(A) + P(B) - P(A and B). You subtract P(A and B) to avoid double-counting outcomes where both events occur. For mutually exclusive events (events that cannot both happen), the formula simplifies to P(A or B) = P(A) + P(B).
Odds in favor of an event are the ratio of favorable to unfavorable outcomes. If the probability is p, the odds are p / (1 - p). Conversely, if the odds are a:b, the probability is a / (a + b). For example, a probability of 0.75 corresponds to odds of 3:1, meaning the event is three times more likely to happen than not.

Related Tools

Combination and Permutation Calculator

Calculate nCr and nPr with step-by-step factorial breakdowns. Understand when order matters.

Statistics and Data

Normal Distribution Calculator

Calculate z-scores, percentiles, and probabilities with an interactive bell curve visualization.

Statistics and Data

Sample Size Calculator

Determine the required sample size for surveys given confidence level, margin of error, and population.

Statistics and Data

Percentage Calculator

Calculate percentages, percentage change, difference, increase, and decrease instantly.

Math and Numbers

Standard Deviation Calculator

Calculate mean, variance, and standard deviation for both population and sample data sets instantly.

Statistics and Data

Grade Calculator

Calculate weighted course grades with customizable assignment categories, points, and what-if grade scenarios.

Education and Academic