,
n number of successes may be lengthy and time consuming To avoid the lengthy
calculations and listing of all the possible cases, for the probabilities  of number of
successes in n-Bernoulli trials, a formula is derived For this purpose, let us take the
experiment made up of three Bernoulli trials with probabilities p and q = 1 – p for
success and failure respectively in each trial The sample space of the experiment is
the set
S = {SSS, SSF, SFS, FSS, SFF, FSF, FFS, FFF}
The number of successes is a random variable X and can take values 0, 1, 2, or 3