binomial
an expression with two terms
A binomial is a type of probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has two possible outcomes, often referred to as success or failure. The term binomial comes from the fact that there are only two possible outcomes for each trial.
The binomial distribution is defined by two parameters: the probability of success, denoted by p, and the number of trials, denoted by n. The probability of getting exactly k successes in n trials is given by the binomial probability formula:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
where n choose k represents the number of ways to choose k items from a set of n items.
The mean or expected value of a binomial distribution is given by np, and the variance is given by np(1-p). The standard deviation is the square root of the variance.
Binomial distributions have many applications in real-life situations, such as in quality control, market research, and medical testing. For example, a company might use a binomial distribution to determine the probability of defective products in a batch, or a doctor might use it to assess the effectiveness of a new treatment.
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