Yes, they are. Consider a uniform random variable between 0 and 1. The probability that the r.v. is in (0, 1) is 1, but 0 and 1 are possible values the r.v. c

Yes, they are. Consider a uniform random variable between 0 and 1. The probability that the r.v. is in (0, 1) is 1, but 0 and 1 are possible values the r.v. can take. This is called “almost surely” and pops up frequently in, for example, stochastic calculus.