Probability Calculator
Calculate various probability statistics for your research or analysis with our comprehensive probability calculator.
How to Use This Calculator
Binomial Probability
Calculate the probability of x successes in n trials with probability p of success on each trial.
- Number of Trials (n): Total number of independent trials
- Probability of Success (p): Probability of success on a single trial (between 0 and 1)
- Number of Successes (x): Number of successful outcomes you're interested in
Normal Distribution
Calculate probabilities for a normally distributed random variable.
- Mean (μ): The mean of the distribution
- Standard Deviation (σ): The standard deviation of the distribution
- X Value: The point of interest on the distribution
Conditional Probability
Calculate P(A|B) and P(B|A) given P(A), P(B), and P(A∩B).
- P(A): Probability of event A
- P(B): Probability of event B
- P(A∩B): Probability of both A and B occurring
Bayes' Theorem
Calculate the posterior probability P(A|B) given the prior P(A) and likelihoods P(B|A) and P(B|¬A).
- P(A) - Prior Probability: Initial probability of A before considering evidence B
- P(B|A) - Likelihood: Probability of observing B when A is true
- P(B|¬A) - False Positive Rate: Probability of observing B when A is false
About Probability Calculations
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. Probability is a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.
Key Probability Concepts
Binomial Probability
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. It is useful for analyzing experiments where there are only two possible outcomes (success/failure).
Normal Distribution
The normal distribution is a continuous probability distribution that is symmetric about the mean. Many natural phenomena follow a normal distribution, making it one of the most important probability distributions in statistics.
Conditional Probability
Conditional probability is the probability of an event occurring given that another event has already occurred. It helps us update our beliefs when we receive new information.
Bayes' Theorem
Bayes' theorem provides a way to update our beliefs about an event based on new evidence. It calculates the posterior probability by incorporating the prior probability and the likelihood of the evidence.