Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 9 / a / ii / Solution

An absolutely continuous probability distribution assigns zero probability to a singleton, because its density has zero integral over that set. Thus $\mathbb{P}(X=x)=0$ for every real $x$, including points where a chosen version of $f$ is nonzero.