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Player A throws a fair coin n+1 times. Player B throws the same coin n times. Player A wins if she throws more heads than Player B. What is the probability of player A winning the game?
My approach has been that since the answer is independent of n, so I chose n=1. So, A can win 3 out 8 times (assuming that Head-Tail is same as Tail-Head) hence the probability is 3/8. Is my assumption correct? What about the approach? How can the solution be generalized?