I have never been very good at probability, and I am confused with this rather simple statement: "BASIC FACT: Let E be any event, and F and G be events such that one and only one of the events F and G will occur. Then P(E) = P(F)*P(E given F) + P(G)*P(E given G)" Where P(E) = the probability of E occurring. And the same for the others. To be honest I don't even understand what it is asking me to do procedurally. What does it mean "E given F"? Is that the probability of E occurring if F occurs? Why is that pertinent? More than that I don't understand the reasoning nor do I have any intuitive inkling as to why this expression would yield the correct answer. Can someone give an example perhaps? (The book I was given just assumes the reader automatically understands this property). Any help would be greatly appreciated.