Binomial Distribution

The binomial distribution is a probability distribution that describes the number of successes in a sequence of independent experiments, each of which has a constant probability of success. It is used to model the number of successes in a sequence of Bernoulli trials, i.e., experiments with two possible outcomes: success or failure.

The binomial distribution is a discrete probability distribution, meaning that it can only take on a finite number of values. The probability of getting exactly k successes in n trials is given by the formula:

P(X = k) = (n! / k!(n - k)!) * p^k * (1 - p)^(n - k)

where:

• n is the number of trials
• k is the number of successes
• p is the probability of success on each trial

The binomial distribution is a special case of the Poisson distribution, which is a continuous probability distribution that describes the number of events that occur in a fixed interval of time or space.

The binomial distribution is used in a variety of applications, such as:

• Predicting the number of defective items in a production run
• Determining the probability of winning a lottery
• Modeling the number of customers who visit a store on a given day

The binomial distribution is a powerful tool for modeling the number of successes in a sequence of independent experiments. It is easy to use and understand, and it can be used to make predictions about a variety of real-world phenomena.