We have a coin with probability of head is p and probability for tail is (1-p). We toss the coin N times, what is the probability that the number of tosses that show head is even?
What I've tried is to sum over all even k's (k= 0,2,4,...) and to sum up the probability that the number of heads is k. Is there a way to elinimate the sum and to give a closed formula?