Independent trials that result in a success with probability p and a failure with probability 1-p are called Bernoulli trials. Let denote the probability that n Bernoulli trials result in an even number of success (0 being considered an even number).
Show that and use this to prove (by induction) that
So denotes the probability that n Bernoulli trials result in an even number of successes p = probability of success p-1 = probability of failure .