Contoh Soal Klasifikasi Naive Bayes

Soal dan jawaban Klasifikasi Naive Bayes yang akan digunakan untuk mengetahui apakah seseorang itu cheat atau tidak.

 

Data

Y = Cheat

X1 = Refund,             X2 = Marital Status,             X3 = Taxable Income

 

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1.     Nomor 1

·       Data: X1 = No,        X2 = Singel,    X3 = 75 K (<80 K)

·       Fakta

P(Y=Yes) = 3/10

P(Y=No) = 7/10

P(X1=No | Y=Yes) = 3/3

P(X1=No | Y=No) = 4/7

 

P(X2=Singel | Y=Yes) = 2/3

P(X2=Singel | Y=No) = 2/7

 

P(X3=75 K | Y=Yes) = 0/3

P(X3=75 K | Y=No) = 3/7

 

P(X1=No, X2=Singel, X3=75 K | Y=Yes) =

{P(X1=No | Y=Yes) * P(X2=Singel | Y=Yes) * P(X3=75 K | Y=Yes) * P(Y=Yes)}

P(X1=No, X2=Singel, X3=75 K | Y=Yes)    = (3/3) * (2/3) * (0/3) * (3/10)

                                                                        = 0

 

P(X1=No, X2=Singel, X3=75 K | Y=No) =

{P(X1=No | Y=No) * P(X2=Singel | Y=No) * P(X3=75 K | Y=No) * P(Y=No)}

P(X1=No, X2=Singel, X3=75 K | Y=No)    =  (4/7) * (2/7) * (3/7) * (7/10)

                                                                      = 0,489796

 

Sehingga

X1 = Refund = No

X2 = Marital Status = Singel

X3 = Taxable Income = 75 K

Y = Cheat = No

2.     Nomor 2

·       Data: X1 = Yes,       X2 = Married,             X3 = 50 K (<80 K)

·       Fakta

P(Y=Yes) = 3/10

P(Y=No) = 7/10

 

P(X1=Yes | Y=Yes) = 0/3

P(X1=Yes | Y=No) = 3/7

 

P(X2=Married | Y=Yes) = 0/3

P(X2=Married | Y=No) = 4/7

 

P(X3=50 K | Y=Yes) = 0/3

P(X3=50 K | Y=No) = 3/7

 

P(X1=Yes, X2=Married, X3=50 K | Y=Yes)          =

{ P(X1=Yes | Y=Yes) * P(X2=Married | Y=Yes) * P(X3=50 K | Y=Yes) * P(Y=Yes)}

P(X1=Yes, X2=Married, X3=50 K | Y=Yes)          = (0/3) * (0/3) * (0/3) * (3/10)

                                                                                  = 0

 

P(X1=Yes, X2=Married, X3=50 K | Y=No)            =

{ P(X1=Yes | Y=No) * P(X2=Married | Y=No) * P(X3=50 K | Y=No) * P(Y=No)}

P(X1=Yes, X2=Married, X3=50 K | Y=No)            = (3/7) * (4/7) * (3/7) * (7/10)

                                                                                  = 0,0734694

Sehingga

X1 = Refund = Yes

X2 = Marital Status = Married

X3 = Taxable Income = 50 K

Y = Cheat = No

3.     Nomor 3

·       Data: X1 = No,        X2 = Married,             X3 = 150 K (>80 K)

·       Fakta

P(Y=Yes) = 3/10

P(Y=No) = 7/10

 

P(X1=No | Y=Yes) = 3/3

P(X1=No | Y=No) = 4/7

 

P(X2=Married | Y=Yes) = 0/3

P(X2=Married | Y=No) = 4/7

 

P(X3=150 K | Y=Yes) = 3/3

P(X3=150 K | Y=No) = 4/7

 

P(X1=No, X2=Married, X3=150 K | Y=Yes)          =

{P(X1=No | Y=Yes) * P(X2=Married | Y=Yes) * P(X3=150 K | Y=Yes) * P(Y=Yes)}

P(X1=No, X2=Married, X3=150 K | Y=Yes)          = (3/3) * (0/3) * (3/3) * (3/10)

                                                                                  = 0

 

P(X1=No, X2=Married, X3=150 K | Y=No)           =

{P(X1=No | Y=No) * P(X2=Married | Y=No) * P(X3=150 K | Y=No)  * P(Y=No)}

P(X1=No, X2=Married, X3=150 K | Y=No)           = (4/7) * (4/7) * (4/7) * (7/10)

                                                                                  = 0,130612

 

Sehingga

X1 = Refund = No

X2 = Marital Status = Married

X3 = Taxable Income = 150 K

Y = Cheat = No

4.     Nomor 4

·       Data: X1 = Yes,       X2 = Divorced,           X3 = 90 K (>80 K)

·       Fakta

P(Y=Yes) = 3/10

P(Y=No) = 7/10

 

P(X1=Yes | Y=Yes) = 0/3

P(X1=Yes | Y=No) = 3/7

 

P(X2=Divorced | Y=Yes) = 1/3

P(X2=Divorced | Y=No) = 1/7

 

P(X3=90 K | Y=Yes) = 3/3

P(X3=90 K | Y=No) = 4/7

 

P(X1=Yes, X2Divorced, X3=90 K | Y=Yes)           =

{ P(X1=Yes | Y=Yes) * P(X2=Divorced | Y=Yes)*P(X3=90 K | Y=Yes) * P(Y=Yes)}

P(X1=Yes, X2Divorced, X3=90 K | Y=Yes)           =  (0/3) * (1/3) * (3/3) * (3/10)

                                                                                  = 0

 

P(X1=Yes, X2Divorced, X3=90 K | No)     =

{ P(X1=Yes | Y=No) * P(X2=Divorced | Y=No) * P(X3=90 K | Y=No) * P(Y=No)}

P(X1=Yes, X2=Married, X3=50 K | Y=No)            = (3/7) * (1/7) * (4/7) * (7/10)

                                                                                  = 0,0244896

Sehingga

X1 = Refund = Yes

X2 = Marital Status = Divorced

X3 = Taxable Income = 90 K

Y = Cheat = No

5.     Nomor 5

·       Data: X1 = No,        X2 = Singel,    X3 = 40 K (<80 K)

·       Fakta

P(Y=Yes) = 3/10

P(Y=No) = 7/10

 

P(X1=No | Y=Yes) = 3/3

P(X1=No | Y=No) = 4/7

 

P(X2=Singel | Y=Yes) = 2/3

P(X2=Singel | Y=No) = 2/7

 

P(X3=40 K | Y=Yes) = 0/3

P(X3=40 K | Y=No) = 3/7

 

P(X1=No, X2=Singel, X3=40 K | Y=Yes) =

{P(X1=No | Y=Yes) * P(X2=Singel | Y=Yes) * P(X3=40 K | Y=Yes) * P(Y=Yes)}

P(X1=No, X2=Singel, X3=75 K | Y=Yes)  = (3/3) * (2/3) * (0/3) * (3/10)

                                                                      = 0

 

P(X1=No, X2=Singel, X3=40 K | Y=No) =

{P(X1=No | Y=No) * P(X2=Singel | Y=No) * P(X3=40 K | Y=No) * P(Y=No)}

P(X1=No, X2=Singel, X3=75 K | Y=No)    =  (4/7) * (2/7) * (3/7) * (7/10)

                                                                      = 0,489796

 

Sehingga

X1 = Refund = No

X2 = Marital Status = Singel

X3 = Taxable Income = 40 K

Y = Cheat = No

6.     Nomor 6

·       Data: X1 = No,        X2 = Married,             X3 = 80 K (<80 K)

·       Fakta

P(Y=Yes) = 3/10

P(Y=No) = 7/10

 

P(X1=No | Y=Yes) = 3/3

P(X1=No | Y=No) = 4/7

 

P(X2=Married | Y=Yes) = 0/3

P(X2=Married | Y=No) = 4/7

 

P(X3=80 K | Y=Yes) = 0/3

P(X3=80 K | Y=No) = 3/7

 

P(X1=No, X2=Married, X3=80 K | Y=Yes)            =

{P(X1=No | Y=Yes) * P(X2=Married | Y=Yes) * P(X3=80 K | Y=Yes) * P(Y=Yes)}

P(X1=No, X2=Married, X3=80 K | Y=Yes)            = (3/3) * (0/3) * (0/3) * (3/10)

                                                                                  = 0

 

P(X1=No, X2=Married, X3=80 K | Y=No) =

{P(X1=No | Y=No) * P(X2=Married | Y=No) * P(X3=80 K | Y=No)  * P(Y=No)}

P(X1=No, X2=Married, X3=80 K | Y=No)             = (4/7) * (4/7) * (3/7) * (7/10)

                                                                                  = 0,0978592

 

Sehingga

X1 = Refund = No

X2 = Marital Status = Married

X3 = Taxable Income = 80 K

Y = Cheat = No

·       Data: X1 = No,        X2 = Married,             X3 = 80 K (>80 K)

·       Fakta

P(Y=Yes) = 3/10

P(Y=No) = 7/10

 

P(X1=No | Y=Yes) = 3/3

P(X1=No | Y=No) = 4/7

 

P(X2=Married | Y=Yes) = 0/3

P(X2=Married | Y=No) = 4/7

 

P(X3=80 K | Y=Yes) = 3/3

P(X3=80 K | Y=No) = 4/7

 

P(X1=No, X2=Married, X3=80 K | Y=Yes)            =

{P(X1=No | Y=Yes) * P(X2=Married | Y=Yes) * P(X3=80 K | Y=Yes) * P(Y=Yes)}

P(X1=No, X2=Married, X3=80 K | Y=Yes)            = (3/3) * (0/3) * (3/3) * (3/10)

                                                                                  = 0

 

P(X1=No, X2=Married, X3=80 K | Y=No) =

{P(X1=No | Y=No) * P(X2=Married | Y=No) * P(X3=80 K | Y=No)  * P(Y=No)}

P(X1=No, X2=Married, X3=80 K | Y=No) = (4/7) * (4/7) * (4/7) * (7/10)

                                                                                  = 0,130612

 

Sehingga

X1 = Refund = No

X2 = Marital Status = Married

X3 = Taxable Income = 80 K

Y = Cheat = No