Coin Toss Off

Coin Toss Off Probability
ProbabilityMedium

Two players, A and B, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B...). The sequence of heads and tails is recorded. If there is a head followed by a tail (HT subsequence), the game ends and the person who tosses the tail wins.

What is the probability that A wins the game?