Two players P_1 and P_2 play a game in which they take turns flipping, independently, a fair coin: First P_1 flips the coin, then P_2 flips the coin, then P_1 flips the coin, then P_2 flips the coin, etc. The game ends as soon as the sequence of coin flips contains either HH or TT. The player who flips the coin for the last time is the winner of the game. For example, if the sequence of coin flips is HT HT HH, then P_2 wins the game. Determine the probability that P_1 wins the game. Show your work