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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 