Probability and possibility

Consider the following four questions:

(a) Is it possible to randomly select a point on a line segment of finite length such that any point is as likely as any other?
(b) Is it possible to randomly select a point on an infinitely extended line such that any point is as likely as any other?
(c) Is it possible to flip a fair coin finitely many times such that it never comes up heads?
(d) Is it possible to flip a fair coin repeatedly such that it never comes up heads?

By "possible", I mean "possible in the real world". To my knowledge, probability theory gives us definitive answers to the first three:

(a) "Yes" because a uniform distribution on a line segment has a well-defined density function such that the corresponding distribution does not violate the axioms of the theory.
(b) "No" because a uniform distribution on the set of integers would violate finite additivity.
(c) "Yes" because the event has positive probability according to the Bernoulli distribution with p = 1/2, we believe that this distribution "exists", and events having positive probability are possible (at least I can't think of a counterexample).

What about (d)? It seems that probability theory has nothing to say one way or the other. I say this because if the criterion is "probability-zero events are not possible" then we could say "no" to (d) (which agrees with what I believe) but would also have to say "no" to (a), which is incorrect.

With all of that as background, I'm asking whether probability theory provides another criterion that I could use to answer question (d). Granted that the experiment of (d) is impossible to perform in real life, and granted that what I'm asking is a meta-mathematical question, nevertheless I still think it's a meaningful one.