Binomial Distribution Calculator

This tool works out binomial probabilities for n independent trials that each succeed with probability p: exactly k successes, at most k, at least k, and the two strict tails either side. A second mode gives the chance the count lands anywhere between two values, both ends included. Every result also carries the mean, variance, standard deviation, the most likely count and the binomial coefficient itself, which switches to scientific notation once it passes fifteen digits. The arithmetic runs on log factorials so that n up to 1000 works without the coefficient overflowing, and the usual assumptions still apply: independent trials, two outcomes, and the same p on every trial.