Difference between p(y=0|x=0) and p(x=0,y=0)

Another Trivial question:

I have been asked to calculate the joint probability i.e. p(X=0,Y=0) and i have been provided by P(Y=0|X=0), is it the same?


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No. Look up the definition of conditional probability and that should answer your question for how they are related.