Problem 3 (20%). Game with chance nodes

In the following tree, square boxes are terminal nodes with given payoff values. A triangle represents a player MAX, and a circle represents a fair coin flip. Consider the following rules:

Rule 1: MAX prefers any action with worst-case outcome of 15 or higher over any action with worst-case outcome lower than 15.

Rule 2: Among two actions with worst-case outcome of 15 or higher, MAX chooses the one with the highest expecti-minimax value.

Rule 3: Among two actions with worst-case outcome lower than 15, MAX chooses the one with the highest worst-case outcome (breaking ties by highest expecti-minimax value).

Fill in a pair of numbers (,) for each non-terminal node (including the root node) in the following game tree, where is the expecti-minimax value and is the value of the worst-case outcome.