# 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.

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