The binomial distribution formula is for any random variable X, given by; P(x:n,p) = nCx x px (1-p)n-x Or P(x:n,p) = nCx x px (q)n-x, where, n is the number of experiments, p is probability of success in a single experiment, q is probability of failure in a single experiment (= 1 – p) and takes values as 0, 1, 2, 3, 4.

Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B). If the probability of one event doesn’t affect the other, you have an independent event. All you do is multiply the probability of one by the probability of another.

There are three characteristics of a binomial experiment. The letter n denotes the number of trials. There are only two possible outcomes, called “success” and “failure,” for each trial. The letter p denotes the probability of a success on one trial, and q denotes the probability of a failure on one trial.

A trinomial is a sum of three terms, while a multinomial is more than three. Quadratic is another name for a polynomial of the 2nd degree.

In statistics, the complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event in such a way that if we know one of these probabilities, then we automatically know the other one. The complement rule comes in handy when we calculate certain probabilities.

The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are appropriately labeled “success” and “failure”.

For large values of n, the distributions of the count Xand the sample proportion are approximately normal. This result follows from the Central Limit Theorem. The mean and variance for the approximately normal distribution of Xare npand np(1-p), identical to the mean and variance of the binomial(n,p) distribution.

Note: The sampling distribution of a count variable is only well-described by the binomial distribution is cases where the population size is significantly larger than the sample size.