5. (5 points) Now suppose we are in a non-deterministic environment with rules as follows. When a player begins their turn they first flip a fair coin (heads probability 5) and if it turns up heads they choose the optimal action. However, if the coin turns upttails they then flip another fair coin to randomly select their action. In this game, what is the probability of a player choosing an optimal action at each node? 6. (5 points) Given the game described in part 5, redraw the game tree as follows. For each tion-terminal node X, introduce a new chance node X'. Let X' be the only successor of X, while the original successors of X are now given to X'. Label the probability on each edge from X' to its successors. These probabilities should sum to 1 for each X 7. (10 points) Using the new game tree in part 6, solve the non-deterministic game. Specifically, provide the erpected game theoretic value of nodes A... G for the new tree. Round your answers to the nearest 2 decimal places (i.e. x.Xx). Hint: this is explained on slide p.58. 3 4 5 NM