The formula for the probability mass function of the Bernoulli distribution is given by: P(X = x) = p^x * (1-p)^(1-x) where X is the random variable representing the outcome of a single Bernoulli trial, x is the possible value of X (either 0 or 1), p is the probability of success (i.e., X = 1), and (1-p) is the probability of failure (i.e., X = 0). This formula works because it describes the probability of a binary event that can either succeed (X = 1) or fail (X = 0) with a fixed probability of success p. The probability of success is constant across all Bernoulli trials, which makes the distribution easy to model and analyze. The formula also satisfies the requirements of a probability mass function (PMF), which must: Be non-negative: The probability of any event cannot be negative, and the formula for the Bernoulli distribution ensures that P(X = x) is always non-negative. 2. Sum to 1: The sum of probabilities for all possible values of X must be equal to 1, and the formula for the Bernoulli distribution ensures that P(X = 0) + P(X = 1) = (1-p) + p = 1.