Independent trials that result in a success with probability p and a failure with probability 1 − p are called Bernoulli trials. Let P_n denote the probability that n Bernoulli trials result in an even number of successes (0 being considered an even number). Show that

P_n = p(1 − P_n−1) + (1 − p)P_n−1 n ≥ 1

and use this formula to prove (by induction) that

Transcribed Image Text:

,, = 1 + (1-2pr