CART selects the split with the LOWEST weighted Gini index.

For example

Parent node: 20 samples, classes = 10 / 10.

Left child: 14 samples, classes = 8 / 6.

Right child: 6 samples, classes = 2 / 4.

We will compute:

Gini of parent

Gini of left child

Gini of right child

Weighted Gini after the split

Gini decrease (how much impurity the split removed)

Step 1:

Parent Gini

So

Parent Gini = 0.5

Step 2:

2) Left child Gini (14 samples: 8 and 6)

Proportions:

Step 3:

3) Right child Gini (6 samples: 2 and 4)

Proportions:

Step 4:

4) Weighted Gini after the split

CART binary split weighted Gini:

Weighted Gini ≈ 0.4761904762

Step 5:

5) Gini decrease (how much impurity reduced)

Gini decrease ≈ 0.0238095238 (≈ 0.024)

Final summary 

Parent Gini = 0.5

Left child Gini ≈ 0.4897959184

Right child Gini ≈ 0.4444444444

Weighted Gini after split ≈ 0.4761904762

Gini decrease ≈ 0.0238095238

Interpretation: the split reduces impurity slightly (by ≈ 0.024). In CART we compare this decrease with other candidate splits and pick the split with the largest decrease.