Feel free to update https://en.wikipedia.org/wiki/Universally_unique_identifier#..., but it does note "This probability can be computed precisely based on analysis of the birthday problem". It does show the formula used.

Wikipedia is correct, AFAICT.

The probability of 1 trillion UUIDs having a collision is,

  def birthday_collision(n, m):
      return 1 - math.e ** (-((n -1) * n) / (2 * m))

  In : birthday_collision(1_000_000_000_000, 2 ** 122)
  Out: 9.403589018575076e-14

That number is roughly the approximation given in Wikipedia.

I.e., at 1T UUIDs, it hasn't happened. For comparison, the odds of being struck by lighting (over a lifetime) is many orders of magnitude greater:

  6.535947712418301e-05