A, B, and C are events from random variables X, Y, and Z respectively. I am having difficulty in understanding the below formula.
P(A,B|C) = P(B|C) * P(A|B,C).
The left hand side of the equation tells - the joint probability of event A and event B given the occurrence of event C. However, I am not sure how to interpret the right most term 'P(A|B,C)'.
Am I supposed to read it as - 'probability of event A given the occurrences of event B and event C?,' i.e., P(A|(B,C))
Or am I supposed to read it as - 'joint probability of event A given the occurrence of event B, and event C?' i.e., P((A|B),C)