2017 Essential Math Competencies in Machine Learning https://www.youtube.com/watch?v=1c25FFm87_c Pr(Y|X)*Pr(X) = Pr(Y,X) = Pr(X|Y)*Pr(Y) Pr(Y|X)*Pr(X) Pr(X|Y) = ------------ Pr(Y) Raygorodsky - 2017 https://www.youtube.com/playlist?list=PL567xYdMCWxYzFfcM1Hafz5tgf1SJWBi- Intuitively, elementary events are independent if P(A|B) = P(A) // knowledge of B gives no new info about the probability of A also P(B|A) = P(B) Multiplication theorem P(A|B)*P(B) = P(A /\ B) // /\ is an intersection From it P(A|B)*P(B) ---------- = P(A)*P(B) P(A /\ B) It is better (because includes cases when P(A) or P(B) can be = 0) So, we can come to definition P(A /\ B) = P(A)*P(B)