I need help some help with the below problems and would appreciate very much if can offer some help.
1) In a competition, 2 teams (A and B) will play each other in the best of 3 games. That is, the final team to win 2 games will be the winner. In the first games, both teams have equal chance of winning. In subsequent games, the probability of team A winning team B given that team A won in the previous game is p and the probability of team A winning team B given that team A lost in the previous game is 1/3.
a) Illustrate the information with an appropriate tree diagram.
b) Find the value of p such that the team A has equal chances of winning and losing the competition.
2) A soccer team of 30 players has 18 Americans and 12 foreigners. Of the
Americans, 10 are midfielders and 8 are defenders. Of the foreigners, 5 are
goalkeepers and 7 are strikers. Four players are chosen at random.
a) If exactly one striker is chosen, find the probability that 3 American are
b) Find the probability that there is exactly one goalkeeper or exactly one defender (or both)