Bernoulli's Formula

Bernoulli's formula is also applied in probability theory, where it plays a crucial role in calculating the probability of success or failure in a series of independent trials with two possible outcomes.

Bernoulli's formula for probability looks as follows:
P(A = k) = C(n, k) * p^k * (1 - p)^(n - k),
where:
P(A = k) - probability that the event A will occur k times in a series of n independent trials,
C(n, k) - number of combinations from n elements by k, also called the binomial coefficient,
p - probability of success in one trial,
(1 - p) - probability of failure in one trial,
k - number of successful trials,
n - total number of trials.

Bernoulli's formula is often used to solve problems related to probabilistic distributions, binomial experiments, as well as in statistics for analyzing random data and modeling probabilistic events.