Then the probability of observing exactly k successes in n independent trials is given by binom nk pk 1 - pn - k dfrac nkn - k pk 1 - pn - k label 340. Binomial probability distributions are very useful in a wide range of problems experiments and surveys. In simple words a binomial distribution is the probability of a success or failure results in an experiment that is repeated a few or many times.
N the number of trials.
If youre seeing this message it means were having trouble loading external resources on our website. In the binomial formula you use the combinations formula to count the number of combinations that can be created when choosing x objects from a set of n objects. P probability of success in a single trial. There are several ways to see that this number is 2 nIn terms of combinations which is the sum of the nth row counting from 0 of the binomial coefficients in Pascals triangleThese combinations subsets are enumerated by the 1 digits of the set of base 2 numbers counting from 0 to 2 n.