Introduction to the Binomial Probability Distribution
In probability theory and statistics, the binomial distribution is a discrete probability distribution that models the number of successes in a sequence of n independent trials, each yielding a binary outcome: success (with probability p) or failure (with probability q = 1 - p). A classic example is flipping a coin multiple times and counting the number of heads. The binomial distribution is fundamental for quality control, medical trials (determining recovery rates), spam filters, and games of chance.
For a distribution to be binomial, four conditions must be met (often remembered by the acronym BINS):
1. Binary: Trials have only two possible outcomes (success or failure). 2. Independent: The outcome of one trial does not affect the others. 3. Number: There is a fixed, pre-determined number of trials n. 4. Same: The probability of success p is constant for each trial.
This calculator evaluates binomial probabilities. By entering the trials n, success probability p, and target success count k, it computes the individual PMF, cumulative CDF, mean, and variance, plotting a complete probability distribution histogram.