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Binomial Simulation Page 3

The Binomial Probability Distribution

Page 3

Binomial Probability Distribution

The goal of this activity is to understand how to use a formula, a table, and a calculator to

determine the probability of a binomial experiment.

Binomial Probability Distribution Function

The probability of obtaining x successes in n independent trials of a binomial experiment,

where the probability of success is p, is given by

n – x

P(x) =

·(1 – p)

, x = 0, 1, 2, …, n

·p

Example: Determine the probability of obtaining 2 successes in 4 independent trials of a

binomial experiment with probability of success 0.35.

Using the Formula

Calculate P(2) with n = 4.

Using Table II

Most statistics books include a table of binomial probabilities, such as Table II in the Appendix

(pages A-2 to A-4). Look down the n column to find 4 and then down the x column to find its

corresponding 2. Scan across that row until you reach the column for the probability p of 0.35.

In a binomial experiment with n = 4 and x = 2, P(2) = _________

Using Technology

The binomial probability distribution function is located in the DISTR menu above the VARS key.

The syntax of the function is given below.

binompdf(n,p,x)

Use the calculator to find the probability.

Robert A. Powers

University of Northern Colorado

Binomial Simulation Page 3