Use this probability calculator to compute simple probability, conditional probability, or Bayesian probability. Get step-by-step solutions instantly.
Select the type of probability, enter the required values, and click Calculate to find the probability value.
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).
Here are the key formulas and concepts in probability theory:
Conditional probability is the probability of an event occurring given that another event has already occurred:
$P(B|A) = \frac{P(A \cap B)}{P(A)}$Bayes' theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event:
$P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B|A) \cdot P(A) + P(B|\neg A) \cdot P(\neg A)}$Used in hypothesis testing, confidence intervals, and data analysis to make inferences about populations based on samples.
Applied in portfolio management, option pricing, insurance calculations, and risk assessment for financial decisions.
Essential in quantum physics, genetics, epidemiology, and experimental design to model uncertainty and natural variation.
Fundamental to many algorithms including Bayesian networks, probabilistic graphical models, and statistical learning methods.
Use decimal probabilities between 0 and 1 for conditional and Bayesian modes. If your source data is in percentages, convert 25% to 0.25 before entering it.
Simple probability compares favorable outcomes to all possible outcomes in a single experiment.
4 / 52
Result: 0.0769 or 7.69%
Conditional probability changes the sample space because one event is already known to have happened.
P(A and B) = P(A) × P(B|A)
If P(A)=0.5 and P(B|A)=0.2, then P(A and B)=0.1
Bayes' theorem updates a prior belief when you observe new information.
(0.8 × 0.1) / ((0.8 × 0.1) + (0.2 × 0.9))
Result: 0.3077 or 30.77%
Simple probability uses the full set of outcomes, while conditional probability recalculates likelihood after assuming another event has already occurred.
A probability represents a share of all possible outcomes, so it cannot be less than 0 or greater than 1.
Use Bayes' theorem when you want to revise the probability of an event after seeing related evidence, such as medical tests, spam filters, or diagnostic models.
The number of favorable cases cannot exceed the total number of possible cases, so that input would not represent a valid probability setup.
