Betty and Bob play a game. They toss a fair coin. If heads occur, then Betty gets a point and if tails occur, then Bob gets a point. The first person to get 3 points wins $ 12. The other person wins $ 0. Betty is winning 2 points to 1. A comet is about to hit the Earth and the game is stopped. It is decided to divide the money ($12) between Betty and Bob. 

Use a tree diagram to show the future possible states of the game and their probabilities. Use the concept of Random Variables (state what it is for the problem and include a probability table) and expected value to compute the appropriate split between Betty and Bob i.e. how much does each get?

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