Find binomial probabilities — the chance of exactly k successes in n trials, plus the cumulative chance. Enter trials, successes, and the success probability.
Usage Tip
When n is large and p near 0.5, the binomial distribution looks almost like a normal curve.
mean = np, sd = √(np(1 − p))
Coin flips and pass/fail tests are classic examples.
The cumulative chance of k or fewer successes is also shown.
Mean is np and standard deviation is the square root of np(1 − p).
The binomial distribution describes the number of successes in a fixed number of independent trials where each trial has the same chance of success, such as the number of heads in ten coin flips or defective parts in a batch. The probability of exactly k successes uses the number of ways to choose k trials from n, multiplied by p to the k and one minus p to the n minus k.
The cumulative probability adds up the chances of k or fewer successes, which answers questions like the probability of at most two defects. The model only applies when the trials are independent and the probability stays the same, so it is a poor fit when you sample without replacement from a small group. The expected number of successes is n times p.