Independent flips of a biased coin that lands on heads with probability is 0.7 are made. Each of two players, A and B has chosen one out of the eight triplets HHH, HHT, HTH, HTT, THH, THT, TTH and TTT, and the player whose triplet occurs first wins. For example, suppose A had chosen HHT and B had chosen THT. Then if the flipped coin shows the sequence HHHT....., A wins, and if the flipped coin shows the sequence TTTHT..., B wins. Since the coin is biased towards heads, the triplet HHH seems to be a good choice.
a) What is the probability that the pattern THH occurs before the pattern HHH?
b) What is the probability that the pattern HTH occurs before the pattern THH?
c) What is the probability that the pattern HHH occurs before the pattern HTH?