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 The probability distribution of the number of successes is as below :
P(X = 0) = P(no success)
= P({FFF}) = P(F) P(F) P(F)
= q q