Basic Probability Notation: Conditional Probability

P(X|Y): probability of X when we know Y and nothing else

P(X|Y) = < P(X=xi|Y=yi) >

P(X and Y) = P(X|Y) * P(Y) = P(Y|X) * P(X)

P(X,Y) = P(X|Y) * P(Y) = < P(X=xi,Y=yi) = P(X=xi|Y=yi) * P(Y=yi) >

P(X|Y) = p does not imply "if Y is true, P(X) = p"

P(X) = P(X| )

P(X|Y) applicable only when Y is only evidence

• P(Cavity|Toothache) = 0.8

• P(A|B) = P(A and B)/P(B)

• P(A and B) = P(A|B) P(B).