Bernoulli Distribution Calculator
Calculate outcome probabilities, mean and variance for a Bernoulli trial.
Bernoulli Distribution
A Bernoulli trial has two outcomes: success with probability p and failure with probability 1−p. Its mean is p and its variance is p(1−p).
Understanding a Bernoulli Trial
A Bernoulli distribution describes a single experiment with only two possible outcomes, often labeled success and failure, with success probability p.
Bernoulli Example
If a component has a 0.98 probability of passing inspection, a Bernoulli model assigns probability 0.98 to pass and 0.02 to fail.
Why It Matters
Bernoulli trials are the basic building blocks of binomial and geometric probability models.
Frequently Asked Questions
How many outcomes are allowed?
Exactly two.
What is the expected value?
It is p when success is coded as 1.
Can p be outside 0 to 1?
No.
Using the Bernoulli Distribution
A Bernoulli distribution models a single trial with exactly two possible outcomes, often described as success and failure. If the probability of success is p, the probability of failure is 1−p. The expected value is p and the variance is p(1−p).
This calculator is appropriate for one yes/no trial such as whether a component passes inspection, a user converts, or a coin toss meets a defined condition. Choose the success event clearly and enter a probability between 0 and 1. For example, p = 0.70 represents a 70% success probability and a 30% failure probability.
For multiple independent Bernoulli trials with the same success probability, the binomial distribution is usually the more appropriate model. Real-world observations may also violate independence or constant-probability assumptions, so confirm that the model matches the situation before interpreting results.
Methodology, Assumptions and Interpretation
A Bernoulli variable represents one trial with success probability p and failure probability 1−p. Its expected value is p and variance is p(1−p); repeated independent Bernoulli trials lead to the binomial model.