Suppose A and B are events in a sample space and that P(A) >1/2 and P(B) >1/2. Prove that P(A intersect B) does not = 0
Recall that $\displaystyle \Pr(A \cap B) = \Pr(A) + \Pr(B) - \Pr(A \cap B)$. Is $\displaystyle \Pr(A \cup B) > 1$ possible? Therefore, what do you conclude?