Explanation:
1/2
Two players, A and B, alternately and independently flip a coin and the first player to get a head wins. Assume player A flips first. If the coin is fair, what is the probability that A wins?
So A only flips on odd tosses. So the probability of winning would be
P=12+(12)212+⋯+(12)2n12
Is that right? It seems that if A only flips on odd tosses, this shouldn't matter. Either A can win on his first toss, his second toss, ...., or his nth toss. So the third flip of the coin is actually A's second toss. So shouldn't it be
P=12+(12)2+(12)3