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Binomial Probability Formula

A probability formula for Bernoulli trials. The probability of achieving exactly k successes in n trials is shown below.

Formula:

n = number of trials
k = number of successes
n – k = number of failures
p = probability of success in one trial
q = 1 – p = probability of failure in one trial

Example:

You are taking a 10 question multiple choice test. If each question has four choices and you guess on each question, what is the probability of getting exactly 7 questions correct?

n = 10
k = 7
n – k = 3
p = 0.25 = probability of guessing the correct answer on a question
q = 0.75 = probability of guessing the wrong answer on a question

See also

Binomial coefficients

 


  this page updated 27-aug-12
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes