Overview
A binomial experiment has a fixed number of independent trials, and each trial has only two possible outcomes. Each of the trials has the same probability of success. The probability distribution is called a binomial distribution.
What Types of Problems Are Binomial?
All the characteristics of a binomial experiment are present, then the distribution will be binomial. A quiz has 8 questions, and each question has 4 alternatives. If a student guesses randomly on every question, what is the probability of getting 5 or more correct? It is a binomial experiment because it has a fixed number of trials (8), and the student is guessing randomly, so each question is independent of every other. Each question can either be answered correctly or incorrectly. In addition, each question has the same probability of success.
What Types of Problems Are Not Binomial?
In a problem that is not a binomial problem, all the characteristics are not present. For example, suppose a standard deck of cards is used, and the number of aces in 5 trials are recorded, but the cards are not replaced after each trial. It is not a binomial distribution, because every trial depends on one another. During the first trial, the population of cards is 52, the second, 51, the third, 50, and the fourth 49, so the trials are not independent. Similarly, if there are three possible outcomes, rather than two, the problem will not be binomial.
What Does a Binomial Distribution Look Like?
A binomial distribution is symmetrical, with the smallest values on either side of the mean, when it is graphed with the probability held constant, the number of trials on the x axis and the function on the y axis. The more trials are done, the more the distribution spreads out, and the more the distribution flattens.
How Is the Binomial Distribution Used?
Many types of real-world situations have a fixed number of independent trials with only two outcomes. For example, treatments often have outcomes of success or failure, basketball players either hit or miss free throws, and potential voters either cast their votes or not in a particular election. Binomial distributions can be used to determine the probabilities of those events and others like them.
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