Problem $1.$ Consider a dataset with three columns of binary attributes $A_1,A_2$ and a binary

label attribute $Y.$ There are eight types of data points in total, and their corresponding

proportions in the dataset are captured in the column $P.$

$($a$)$ What is the GINI index of the dataset?

$($b$)$ What is the GINI index of the split on $A_1$ and that on $A_2$ respectively?

$($c$)$ Jonstruct a decision tree of exactly five nodes for the dataset using Hunt's algorithm.

$($d$)10\%$ What is the accuracy of the decision tree built on $($c$)?$