Binomial Distribution

The binomial distribution is a 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.

$P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}$

• $X$ is the random variable representing the number of successes
• $n$ is the number of trials (a fixed value)
• $k$ is the number of successes ($k = 0, 1, 2, \ldots, n$)
• $p$ is the probability of success in each trial ($0 \ge p \ge 1$)

Probability of success in 0 trials with probability of 0.