The following table gives a data set for deciding whether to play or cancel a ball game, depending on the weather conditions:

1) At the root node for a decision tree in this domain, what would the information gain associated with a split on the Outlook attribute? What would it be for a split at the root on the Humidity attribute? (Use a threshold of 75 for humidity (i.e., assume a binary split: humidity 75.)

2) Suppose you build a decision tree that splits on the Outlook attribute at the root node. How many children nodes are there are at the first level of the decision tree? Which branches require a further split in order to create leaf nodes with instances belonging to a single class? For each of these branches, which attribute can you split on to complete the decision tree building process at the next level (i.e., so that at level 2, there are only leaf nodes)? Draw the resulting decision tree, showing the decisions (class predictions) at the leaves.

F) Humidity (%) windy? Class 70 Outlook |Temp ( sunny75 sunny 80 sunny 85 sunny 72 sunny69 rue Play true false Don't Play falseDon't Play false Play rue Play false Play rue Play false Play true true false Play false Play false Play 90 85 95 70 Don't Play overcast 72 90 overcast 83 78 overcast 64 65 overcast 81 75 71 65 75 68 70 80 70 80 80 96 Don't Play Don't Play rain rain rain rain rain