3. This question considers pruning in games with chance nodes. Here is the complete game tree for a very simple game. Assume that the leaf nodes are to be evaluated in left to right order, and that before a leaf node is evaluated, we know nothing about its value, that is the range of possible values is to . [20 Points] a. Mark the values of all the internal nodes and indicate the best move at the root with an arrow. b. True/False: Given the values of the first six leaves (from the left), the seven and eight leaf is irrelevant and need not be evaluated. c. True/False: Given the values of the first seven leaves (from the left), the eight leaf is irrelevant and need not be evaluated. d. Now suppose all the leaf nodes values are known to lie between 2 and 2 inclusive. After evaluating the first two leaves, what range of values can be deduced for the left-hand chance node? e. Circle all the leaves that need not be evaluated under the assumption in (d)