5. (Total: 12 points) Independent flips of a biased coin that lands on heads with probability 0.8 are made. Each of two players, A and B, had chosen one out of the eight triplets: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT)} where H represents a head and T represents a tail, and the player whose chosen triplet occurs first wins. Suppose A had chosen HHT and B had chosen THT. If the flipped coin shows, for example, the sequence HHHT... A wins; and if the flipped coin shows, for example, the sequence TTTHT.. B wins. What is the probability that A wins?