$\backslash$table$[[$Age$,$Salary,$\backslash$table$[[$Education$],[$level$]],$Class,Prob$($yes$)],[$Young$,40$K$,$PhD$,$Yes,$60\%],[$Old$,35$K$,$BSc$,$No$,33\%],[$Young$,36$K$,$MSc$,$Yes,$57\%],[$Old$,38$K$,$BSc$,$No$,39\%],[$Young$,32$K$,$MSc$,$Yes,$55\%],[$Old$,34$K$,$MSc$,$No$,42\%],[$Young$,42$K$,$PhD$,$Yes,$71\%],[$Old$,39$K$,$BSc$,$No$,40\%],[$Old$,31$K$,$PhD$,$Yes,$52\%],[$Young$,41$K$,$BSc$,$No$,31\%],[$Old$,45$K$,$BSc$,$Yes,$54\%],[$Young$,44$K$,$BSc$,$No$,32\%]]($a$)$ Consider the following dataset where each row $($instance$)$ represents an

applicant to a loan, described by three predictive attributes $($Age$,$ Salary,

Education level$)$ and the Class variable, indicating whether or not an applicant

was granted a loan $($class labels $$yes$$ and $$no$).$ The column Prob$($yes$)$ shows

the probability that each applicant belongs to the class $$yes$,$ computed by a

certain classification algorithm.

Age Salary Education

level

Class Prob$($yes$)$

Young $40$K PhD Yes $60\%$

Old $35$K BSc No $33\%$

Young $36$K MSc Yes $57\%$

Old $38$K BSc No $39\%$

Young $32$K MSc Yes $55\%$

Old $34$K MSc No $42\%$

Young $42$K PhD Yes $71\%$

Old $39$K BSc No $40\%$

Old $31$K PhD Yes $52\%$

Young $41$K BSc No $31\%$

Old $45$K BSc Yes $54\%$

Young $44$K BSc No $32\%$

Assume that Age is a sensitive $($protected$)$ attribute, i$.$e$.,$ the distribution of the

class labels $$yes$$ and $$no$$ should not depend on the applicant$$s age. Note

that in this dataset the distribution of the label $$yes$$ is unfair with respect to

the attribute Age, since $2/3(4$ out of $6)$ of $$young$$ applicants have the label

$$yes$,$ whilst only $1/3(2$ out of $6)$ of $$old$$ applicants have the label $$yes$.$

Consider the use of the data massaging technique to modify the class labels

of two applicants $($instances$)$ of this dataset, in order to make this dataset

fairer with respect to Age. Describe the application of this technique to this

dataset. Your answer must show all the steps that you performed, as well as

the final result $($which applicants had their class labels changed$)$