A classification tree is being constructed to predict if an insurance policy will lapse. A random sample of $100$ policies contains $30$ that lapsed. You are considering two splits: Split $1$: One node has $20$ observations with $12$ lapses and one node has $80$ observations with $18$ lapses. Split $2$: One node has $10$ observations with $8$ lapses and one node has $90$ observations with $22$ lapses. The total Gini index after a split is the weighted average of the Gini index at each node, with the weights proportional to the number of observations in each node. The total entropy after a split is the weighted average of the entropy at each node, with the weights proportional to the number of observations in each node. Determine which of the following statements is$/$are true? I. Split $1$ is preferred based on the total Gini index. II$.$ Split $1$ is preferred based on the total entropy. III. Split $1$ is preferred based on having fewer classification errors.