1. The nominal predictor is A, and it has three categories: Sugar, Pepper, and Salt. The binary target variable is B, and it has two categories: No and Yes. We have already summarized the data into the following cross-tabulation table of A by B.

A	B
No	Yes	Total
Sugar	5	20	25
Pepper	32	8	40
Salt	7	28	35
Total	44	56	100

1. We will build a classification tree using the CART algorithm with theGini Index.The maximum depth is one.
2. What is the optimal way to split the categories of the nominal predictor A into two branches?

	A.	Branch 1: Pepper and Salt Branch 2: Sugar
	B.	Branch 1: Pepper and Sugar Branch 2: Salt
	C.	Branch 1: Salt and Sugar Branch 2: Pepper
	D.	None of the Above

1. What is thereductioninGini Index(from the Root Node) for the optimal split? Please round your answer up to the seventh decimal place.