Probability or no probability???

If x,y are chosen randomly in the interval (a,b), The probability that x=y is 0, but is still possible.

Another example involves picking a random real number on any interval $[a,b]$ where $a \lt b$ . Since on any such interval the number of irrationals is uncountably infinite and the number of rationals countably infinite, the probability of choosing a rational is $0$ , even though it is indeed possible to choose one.

One of the scenarios that I have in mind is the following:

We know that the total number of real numbers between 0 and 1(or any two integral numbers) is infinite

So if A asks B to pick any number between 0 and 1,even though there is a very very slight chance of guessing the correct number,mathematically speaking

Probability=[number of favourable scenarios/number of all possible scenarios], which in this case is 1/infinite

If you know your precal/calc, you can write this as the limit as x->infinity of 1/x = 0. Essentially, 1 divoded by a very big number gets very close to zero, so… 1 divided by infinity,mathematically speaking, is equal to 0

Therefore the answer is Yes