Very basic probability question (inequalities) This seems intuitively obvious to me, yet I can't seem to convince myself algebraically that it is.
Let $B,C>0$
Given $P(X)=P(B>C)$
Is it true that $P(X) \leq P(B \geq C)$ ? If so, what is the easiest was to demonstrate it ?
PS this is not homework.

Yes, it is: $P(B\geq C) = P(B>C)+P(B = C) = P(X)+P(B=C)\geq P(X)$.
