The opposite is true. Take the interval [0, 1], "sample a random real number x" from it. P(x is rational) = 0, P(x is irrational) = 1.
Informally, the overwhelming majority of real numbers are irrational.
Informally, the overwhelming majority of real numbers are irrational.
Likewise, if you take any two randomly generated list of decimal digits, at some point there will be a digit in the same place that is different between the two. At that point, you can construct a rational between the two by choosing the smaller digit and then adding "1000....".
But yeah, it's kind of weird.
You can keep going with things that sound weird:
There are infinitely many rationals between any two irrational numbers.
There are as many rational numbers between any two finite irrational numbers as there are between positive and negative infinity.