We have a domain where there is only one feature, X, which is binary. The domain...
We have a domain where there is only one feature, X, which is binary. The domain has also a category label Y, which is binary as well.
Given a Naive Bayes model with following parameters:
P(X=T|Y=T) = 0.2
P(X=F|Y=F) = 0.6
P(Y = T) = 0.7
Given an instance X = T, what is the probability that its label is True calculated by the model?
Homework Answers
here P(X=T)=P(Y=T)*P(X=T|Y=T)+P(Y=F)*P(X=T|Y=F)=0.7*0.2+(1-0.7)*(1-0.6)=0.14+0.12=0.26
hence P(Y=T|X=T)=P(Y=T)*P(X=T|Y=T)/P(X=T)=0.7*0.2/0.26=0.538462
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