Probability Calculator

Use this probability calculator to compute simple probability, conditional probability, or Bayesian probability. Get step-by-step solutions instantly.

Probability Calculator

Select the type of probability, enter the required values, and click Calculate to find the probability value.

What is Probability?

Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 0 and 1. A probability of 0 indicates impossibility, while a probability of 1 indicates certainty.

For example, the probability of rolling a 6 on a fair die is 1/6 (approximately 0.167), because there is 1 favorable outcome (rolling a 6) out of 6 possible outcomes. Similarly, the probability of drawing an ace from a standard deck of 52 cards is 4/52 = 1/13 (approximately 0.077).

Probability Formulas

Here are the key formulas and concepts in probability theory:

Simple Probability

$P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

Bayesian Probability

Bayes' theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event:

$P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B|A) \cdot P(A) + P(B|\neg A) \cdot P(\neg A)}$

Applications of Probability

Statistics and Data Analysis

Used in hypothesis testing, confidence intervals, and data analysis to make inferences about populations based on samples.

Finance and Risk Assessment

Applied in portfolio management, option pricing, insurance calculations, and risk assessment for financial decisions.

Science and Research

Essential in quantum physics, genetics, epidemiology, and experimental design to model uncertainty and natural variation.

Artificial Intelligence and Machine Learning

Fundamental to many algorithms including Bayesian networks, probabilistic graphical models, and statistical learning methods.

How to Use This Calculator

  1. Select the type of probability you want to calculate (simple, conditional, or Bayesian).
  2. For simple probability, enter the number of favorable outcomes and total possible outcomes.
  3. For conditional probability, enter the probability of event A and the probability of event B given A.
  4. For Bayesian probability, enter the prior probability, likelihood, and marginal likelihood values.
  5. Click 'Calculate' to compute the probability and see the step-by-step solution.