Suppose that A & B are events in a sample space and that P(A) > (1/2) and P(B) > (1/2).
Prove that P(A "intersection" B) does not equal 0.
similar to:
limit as n approaches zero, we know that P( A intersection B) must be greater than zero, though it may be close ( as the aforementioned limit). And thus, we see that it also cannot equal zero!
I think I may have been a bit vague, but let me know if that sounds right.
I think I have the right approach now.
Thanks
I dont understand what you are saying
But Plato nearly answered your question
$\displaystyle 1 \ge P(A \cup B) = P(A) + P(B) - P(A \cap B) > \left( {1/2} \right) + \left( {1/2} \right) - P(A \cap B) \Rightarrow 0 < P(A \cap B)$
Thus we see it is greater than 0. So it cannot be 0