In the diagram below, we have two attributes, A and B, each with two values (1 a
ID: 3362043 • Letter: I
Question
In the diagram below, we have two attributes, A and B, each with two values (1 and 2). The numbers in the matrix are the number of instances.
We will use these numbers in the questions that follow
What is the total number of instances?
What is P(A=1)?
For A=2, B=1, What is P(A|B)?
For A=2, B=1, what is P(B)?
For A=2, B=1, what is P(A,B)?
For A=1, B=1, what is P(A,B)?
Using the sum rule, what probabilities do we need to sum in order to get the marginal probability of P(B=1)?
P(B=2) and P(A=1) and P(A=2)Explanation / Answer
Ans:
1)
i)Total number of instances=10+20+30+40=100
ii)For A=2, B=1
P(A=2|B=1)=P(A=2,B=1)/P(B=1)=40/50=0.8
iii)P(B=1)=(10+40)/100=50/100=0.5
iv)For A=2, B=1,
P(A=2,B=1)=40/100=0.4
v)For A=1, B=1,
P(A=1,B=1)=10/100=0.1
2) probabilities needed to sum in order to get the marginal probability of P(B=1):
P(B=1)=P(A=1,B=1) + P(A=2,B=1)
Hence,correct answer is P(A=1,B=1) and P(A=2,B=1)