The law of total probability extends to the case of conditioning on events generated by continuous random variables. Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} be a probability space. Suppose X {\displaystyle X} is a random variable with distribution function F X {\displaystyle F_{X}} , and A {\displaystyle A} an event on ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} .