What Every Leaf Has to Earn

A loan-approval tree was grown on 136 past applicants and left completely unpruned. The table shows every node: how many training applicants reached it, and how they split between Approve and Reject.

Every leaf predicts its majority class, so the applicants in its minority are its errors.

Cost-complexity pruning scores a tree $T$ by

$$\text{cost}_\alpha(T) = \text{errors}(T) + \alpha \times \text{leaves}(T)$$

where $\alpha \ge 0$ is a price charged for every leaf. Collapsing a question node $t$ replaces its whole branch with one leaf that predicts $t$'s majority class. That trade starts to pay once $\alpha$ reaches

$$g(t) = \frac{(\text{errors if } t \text{ were a leaf}) - (\text{errors in } t\text{'s current leaves})}{(\text{number of } t\text{'s current leaves}) - 1}$$

Weakest-link pruning raises $\alpha$ from $0$. It computes $g$ for every question node in the current tree, collapses the node with the smallest $g$ (that $g$ is the value of $\alpha$ at which the collapse happens), then repeats the whole process on the smaller tree.

At what value of $\alpha$ does the second collapse happen? Give your answer to 2 decimal places.