Solve Gini index for

Case (1): 4Y / 8N

Step 1: Given

• Y = 4
• N = 8
• Total = 12

Step 2: Probabilities

Step 3: Apply Formula

✅ Result

Gini Index (4Y/8N)=0.44

Gini Index for(Case 2) 8Y / 2N

Given:

• Yes (Y) = 8
• No (N) = 2
• Total = 10

Step 1: Write the Gini Index Formula

Step 2: Calculate Probabilities

Step 3: Substitute Values

Step 4: Final Answer

Gini Index=32/100=0.32

Final Result

Case	Y	N	Gini Index	Node Type
8Y / 2N	8	2	0.32	Impure (but less impure)

Important Concept (Exam Point)

• Gini = 0 → Pure node
• Gini = 0.5 → Maximum impurity (binary class)
• Lower Gini value means purer node

👉 Since 0.32 < 0.44 (root) and < 0.5,
8Y / 2N is purer than 4Y / 8N or 3Y / 3N.

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🔹 Comparison Table

Case	Y	N	Gini Index	Purity
4Y / 8N	4	8	0.44	More impure
8Y / 2N	8	2	0.32	More pure

Final Conclusion 

Lower Gini Index ⇒ Purer Node

• Higher Gini Index ⇒ More Impure Node

Since 0.32 < 0.44,
8Y / 2N is purer than 4Y / 8N

CART algorithm will prefer the split with Gini = 0.32.