If A and B are two events such that $P(A) > 0$ and $P(A) + P(B) > 1$, then is
$P(B/A) \geq 1 - \frac{P(B')}{P(A)} ?$
I could only get far P(B/A) = $\frac{P(A \cap B )}{P(A)}$ = $\frac{P(A) + P(B) - P(A \cup B)}{P(A)}$ > $\frac{1 - P(A \cup B)}{P(A)}$
Is this enough to say that the above statement isn't true?
Hint: Your inequality (to be proved) is equivalent to, after a simplification:
$$P(A\cap B)\geq P(A)+P(B)-1$$
The RHS is greater than zero since $P(A)+P(B)>1$. Hence, we have to prove $P(A\cap B)>0$.
The last inequality is obviously true, since $P(A) + P(B) > 1$ is not possible for mutually exclusive events.