4.10 Introduction to the Binomial Distribution

You need to know how to find probabilities of binomial variables using simulation data or your calculator. Using random number generators is crucial.

A binomial setting arises when we perform n independent trials of the same chance process and count the number of times that a particular outcome called a success, occurs. Failure is defined as 1 minus the probability of success. 

The count of successes in a binomial setting is a binomial random variable. The probability distribution of X is a binomial distribution. The possible values of X are 0, 1, 2, 3, …,n. Any binomial distribution is completely specified by two numbers: the number of trials of the chance process and the probability p of success on each trial. 

Binomial coefficients: The number of ways to arrange k successes in n trials is given by the binomial coefficient or n over k without a fraction bar. 

To find binomial variable probability, use the following formula or use the calculator function of binomCDF/PDF.

BinomialCDF is for cumulative distribution frequency or when you want to include the boundary and every value that came before it. BinomialPDF is for point distribution frequency or when you’re looking for strictly one value.

🎥Watch: AP Stats - Probability: Random Variables, Binomial/Geometric Distributions