Binomial Formula and Binomial Probability
The binomial probability refers to the probability that a binomial experiment results in exactly x successes.Given x, n, and P, we can compute the binomial probability based on the binomial formula.
Binomial Formula. Suppose a binomial experiment consists of n trials and results in x successes. If the probability of success on an individual trial is P, then the binomial probability is:
\[b(x; n,P)= C_{n}^{x}\times P^{x}\times \left ( 1-P \right )^{n-x} \]
or
\[b(x; n,P)= \frac{n!}{x!(n-x)!} \times P^{x} \times (1-P)^{n-x} \]
