Question: Play this game, please. OK, friends, we've got a little deal for you. We have a fair coin (heads and tails each have probability 1/2). Toss it twice. If two heads come up, you win right there. If you get any result other than two heads, we'll give you another chance: toss the coin twice more, and if you get two heads, you win. (Of course, if you fail to get two heads on the second try, we win.) Pay us a dollar to play. If you win, we'll give you your dollar back plus another dollar.
(a) Make a tree diagram for this game. Use the diagram to explain how to simulate one play of this game.
(b) Your dollar bet can win one of two amounts, 0 if we win and $2 if you win. Simulate 50 plays, using Table A, starting at line 125. Use your simulation to estimate the expected value of the game.