Homework Answers
a) P(LikeRockMusic=NO)=4/9 [ Explanation: There are total 9 records. Out of it 4 records are LikeRockMusic=NO. Hence the probability is 4/9]
b) P(UniDegree=YES|class=2) =1/2 [ Explanation: There are 2 records with class=2. Out of it 1 record is UniDegree=YES. Hence the probability is 1/2]
c) P(LikeRockMusic=YES|UniDegree=NO)= 1/4 [Explanation: There are 4 records with UniDegree=NO. Out of it 1 record is LikeRockMusic=YES. Hence the probability is 1/4]
d) There are three classes 1,2,3.
We need to calculate the following. The test sample given has UniDegree=YES and LikeRockMusic=YES.
P(Class 1)=3/9=1/3 [ Explanation: There are 3 records with class=1 out of 9 records. Hence the probability is 1/3]
P(Class 2)=2/9 [ Explanation: There are 2 records with class=2 out of 9 records. Hence the probability is 2/9]
P(Class 3)=4/9 [ Explanation: There are 4 records with class=3 out of 9 records. Hence the probability is 4/9]
Next we need to compute
P(UniDegree=YES| class=1) =2/3 [Explanation: There are 2 records with UniDegree=YES in class 1. Class 1 contains 3 records Hence the probability is 2/3]
P(UniDegree=YES|class=2)= 1/2 [Explanation: There is 1 record with class=2 and UniDegree=YES. Class 2 contains 2 records. Hence the probability is 1/2]
P(UniDegree=YES|class=3) =2/4 [Explanation: There are 2 records with UniDegree=YES in class 3. Class 3 contains 4 records Hence the probability is 2/4]
P(LikeRockMusic=YES|class=1)=3/3=1 [Explanation: There are 3 records with LikeRockMusic=YES in class 1. Class 1 contains 3 records Hence the probability is 3/3]
P(LikeRockMusic=YES|class=2)=1/2 [Explanation: There is 1 record with LikeRockMusic=YES in class 2. Class 2 contains 2 records Hence the probability is 1/2]
P(LikeRockMusic=YES|class=3)=1/4 [Explanation: There is 1 record with LikeRockMusic=YES in class 3. Class 3 contains 4 records Hence the probability is 1/4]
Compute the following for Class 1
P(UniDegree=YES| class=1) =2/3 * P(LikeRockMusic=YES|class=1)=3/3=1 = 2/3*1=2/3
Compute the following for Class 2
P(UniDegree=YES|class=2)= 1/2 * P(LikeRockMusic=YES|class=2)=1/2 = 1/2* 1/2 = 1/4
Compute the following for Class 3
P(UniDegree=YES|class=3) =2/4 =1/2 * P(LikeRockMusic=YES|class=3)=1/4 = 1/2*1/4=1/8
The final probabilities can be calculated for Class 1 as follows.
P(Class 1)=3/9=1/3 *[ P(UniDegree=YES| class=1) =2/3 * P(LikeRockMusic=YES|class=1)=3/3=1 = 2/3*1=2/3]
=1/3 * 2/3=2/9
The final probabilities can be calculated for Class 2 as follows.
P(Class 2)=2/9 * [ P(UniDegree=YES|class=2)= 1/2 * P(LikeRockMusic=YES|class=2)=1/2 = 1/2* 1/2 = 1/4]
=2/9* 1/4 = 2/36=1/18
The final probabilities can be calculated for Class 3 as follows.
P(Class 3)=4/9 *[ P(UniDegree=YES|class=3) =2/4 =1/2 * P(LikeRockMusic=YES|class=3)=1/4 = 1/2*1/4=1/8]
=4/9 *1/8 = 4/72=1/18
Since both Class 2 and Class 3 both have the maximum value of 1/18, the test sample belongs to Class 2 or Class 3
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