The binomial distribution formula is: b(x; n, P) = n C x * P x * (1 – P) n – x Where: b = binomial probability x = total number of “successes” (pass or fail, heads or tails etc.) P = probability of a success on an individual trial n = number of trials Note: The binomial distribution formula can also be written in a slightly different way, because n C x = n! / x!(n – x)! (this binomial distribution formula uses factorials (What is a factorial? ). “q” in this formula is just the probability of failure (subtract your probability of success from 1). Using the First Binomial Distribution Formula The binomial distribution formula can calculate the probability of success for binomial distributions. Often you’ll be told to “plug in” the numbers to the formul...