Free online probability calculator for binomial, normal, and Poisson distributions. Calculate probabilities, distributions, and statistical events with step-by-step solutions.
Probability theory is a fundamental branch of mathematics that deals with the analysis of random phenomena. Our probability calculator helps you compute the likelihood of various events using different probability distributions. Whether you're a student learning statistics, a researcher analyzing data, or a professional making decisions under uncertainty, our tool provides accurate probability calculations with detailed explanations.
This comprehensive tool supports multiple probability distributions, including binomial, normal, and Poisson, each designed for specific types of statistical problems and real-world applications.
Total number of independent trials (must be a non-negative integer)
Probability of success in each trial (between 0 and 1)
Exact number of successes to calculate probability for (integer between 0 and n)
Enter values above to see the binomial distribution probability
Calculating the probability of getting exactly 3 heads in 5 coin flips: n=5, p=0.5, k=3
Finding the probability that a person's height is between 160cm and 180cm in a population with mean 170cm and std dev 10cm
Calculating the probability of receiving 4 emails per hour, given an average rate of 3 emails per hour
Determining the probability of finding at most 2 defective items in a sample of 20 from a batch with 5% defect rate
Students and educators solving probability problems and understanding statistical concepts
Researchers analyzing experimental data and conducting statistical tests
Decision-making under uncertainty, risk assessment, and quality control
A probability distribution describes how the values of a random variable are distributed. It provides a mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.
Used when there are exactly two mutually exclusive outcomes of a trial - "success" and "failure". It describes the probability of having exactly k successes in n independent Bernoulli trials with probability p of success on each trial.
Also known as the Gaussian distribution, it's a continuous probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.
A probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range. It helps us understand the behavior of random phenomena.
Use binomial distribution when you have a fixed number of independent trials, each with the same probability of success, and you're interested in the number of successes in those trials.
Normal distribution is continuous and symmetric, often used for naturally occurring variables. Poisson distribution is discrete and used for counting the number of events that occur in a fixed interval of time or space.
Yes, the probability values calculated by this tool can be used as part of hypothesis testing procedures, such as determining p-values for statistical tests.
The results show the probability of your specified event occurring. Values closer to 0 indicate unlikely events, while values closer to 1 indicate likely events. The tool also provides detailed explanations of the calculations.
Absolutely! This calculator is designed to assist students, teachers, and researchers with academic probability problems and statistical analysis.