I have some understanding problems with what the prof taught me today. I am just going to break it down and we can discuss, perhaps: a. the sum of the collectively exhaustive events must equal 1. I know that if an event is both collectively exhaustive and mutually exclusive it should cover the entire space and it's sum is 1. But if it's just collectively exhaustive, wouldn't there be a chance that it might overlap other events so making it not equal to 1? b. if A and B are mutually exclusive, A(complement) and B(complement) are mutually exclusive. I think this is not always true, because say A doesn't intersect with B, then the complements of both A and B should intersect. or I might be wrong in this. c. If A and B are independent, then A(complement) and B(complement) are are also independent. I really didn't get this one. I hope somebody will be able to help me out with one at least if not all.