For Susan Athena:
Had a chance to review your answer.
Not totally sure what you mean by "Events which are mutually exclusive cannot be independent and vice-versa."
It's the "vice- versa" part that is bothering me.
I have been able to prove M implies not I and also I implies not M.
Your vice-versa part sounds like M impies not I and also not I imlies M.
Could you please clarify?
Also, how do we handle this situation?
Once again let's toss a single fair die(sample space 1,2,3,4,5,6) once. Let event A = roll a 7 and event B = roll an 8. Clearly P(A and B) =0 and P(A) x P(B) = 0. This seems to imply that A and B are both mutually exclusive and independent. I guess this is just an exception???