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, 442 CHAPTER 20 The House Edge: Expected Values 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.