Binomial Distribution

Modeling the number of successes in a sequence of independent trials.

The "Coin Flip" Distribution

The Binomial Distribution is a discrete probability distribution that models the number of successes in a fixed number of independent 'Bernoulli' trials, where each trial has only two possible outcomes: success or failure.

Think of flipping a coin 10 times and counting the number of heads. In finance, this could model the number of winning trades in a month (where each trade is a trial), or the number of portfolio companies that meet their earnings target in a quarter.

The Formula
The probability of observing exactly 'k' successes in 'n' trials is:
P(X=k)=(nk)pk(1−p)n−kP(X=k) = \binom{n}{k} p^k (1-p)^{n-k}
  • (nk)\binom{n}{k} is the number of combinations, "n choose k".
  • nn is the number of trials.
  • kk is the number of successes.
  • pp is the probability of success on a single trial.
Interactive Binomial Distribution
Adjust the number of trials (n) and the probability of success (p) to see how the shape of the distribution changes.