# Simplifying probablity equation based on its cumulative distribution function (CDF)

How can I simplify the following probability equation based on cumulative distribution function of X:

P(X>a)>b


which P is the probability of X and X has a known probability distribution function and a & b are real positive numbers.

• Do you the definition of a CDF? – user190080 Jul 31 '18 at 14:48
• Back to the problem: Start with $X$ has cdf $F_X(X \le a) = 1 - P(X > a).$ You can get other, possibly useful, relationships from there. Not sure whether I'd call the 'simplifications'. – BruceET Aug 1 '18 at 4:40

$$P(X>a)>b$$
$$-P(X>a)<-b$$ $$1-P(X>a)<1-b$$
$$P(X \le a)<1-b$$
$$F_X(a)<1-b$$