Related: math.stackexchange.com/q/41107

See also stats.stackexchange.com/a/481875/262994

@TaW: What's wrong with that statement? It's perfectly correct under generally accepted mathematics.

Oh yeah? Try to pick a number then!

@TaW: I’m not sure what you mean by that. Perhaps you can write a more detailed answer to explain why the probability isn’t zero, rather than making cryptic statements in the comments.

There is nothing cryptic in my comments. The fact that there is an infinite number of numbers to choose from gives each one a probability os 1:infinity, i.e. 0. But you still can pick one. Falling into logical infinity traps has a long history, but still.. - Another way of putting it is: The fact that we cannot know a fact (precise speed) doesn't make it disappear.

Same with any continuous variable. What is the probability that a randomly chosen person is exactly 180.00000000000000000000000000000000000000000000000000000000‌​00000000000000000000‌​00000000cm tall?

Related: Zeno's arrow paradox

The key insight here is that in a continuous distribution, $P=0$ means "almost never", not "never". Here it has nothing to do with whether we can physically determine the velocity, it's just that probability over continuous distributions is a measure, as a kind of extension of "size" or "length" to infinite sets, which allows for seemingly unintuitive things like "a set that has elements in it but has measure 0", such as in this case. (In fact, not only is the probability of any velocity 0, so is the probability of any group of eg. five or ten velocities, yet they can still occur.)

$1/\infty = 0$ is perfectly true for most reasonable definitions of "=", "/", etc., just not perhaps the most strict definitions commonly in use.

The clash of Descartes and Hume rages on

Total Energy of all the molecules is fixed, so a single molecule can't cross a certain maximum speed. There will be an upper bound

Velocity of a particle depends on the initial Energy given to it, if we are talking about a single isolated particle. The particle can't choose among the infinite possibilities. It's given to it from outside.

@Syed Jaffri, between 1 and 2 there are infinite choices.

@YasirSadiq, I think velocity will depend on the energy given to it.(E=1/2mv^2) There's no question of choice.