(The Problem of Points) Betty and Bob play a game. They toss a fair coin. If heads occurs, Betty gets a point and if tails occurs Bob gets a point. The first person to get 3 points wins $ 20. The other person wins $ 0. Betty iswinning 2 points to 1.

A comet is about to hit the Earth and the game is stopped. It is decided to divide the money ($20) 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?