The Superbowl institutes a new way to determine which team receives the kickoff first. Thereferee chooses with equal probability one of three coins. Although the coins look identical, they have probability of heads 0.1, 0.5 and 0.9, respectively. Then the referee tosses the chosencoin 3 times. If more than half the tosses come up heads, one team will kick off; otherwise, theother team will kick off. If the tosses resulted in the sequence H, T, H, what is the probabilitythat the fair coin was actually used