Two equally skilled people play a game in which the first to carn 10 points wins $100 and each player has an equal chance of winning a point. At some point in the game, however, one of the players has to leave and the game must be stopped. If the game score is 9 points to 7 how should the $100 be divided between the two players? This diagram shows the number of ways the game could have been completed.
Use this diagram to help calculate the probability that:
i player A wins the game
ii player B wins the game.
Based on your answers from part a, describe how the $100 should be divided between players A and B.
Investigate how the $100 should be divided between players A and B if the game is stopped with the following number of points. You will need to draw a new tree diagram cach time.
i player A: 8 points, player B: 7 points
ii player A: 7 points, player B: 7 points
iii player A: 8 points, player B: 6 points
IV player A: 6 points, player B: 7 points