How to do the impossible at home

Impossible probabilities

Recently I enjoyed a video entry (in Russian) by the blogger Lex Kravetski, who discussed logical manipulations with probabilities in debates. Indeed, is it not tempting to interpret an event with an extremely low probability as impossible? Lex has a really fun way of making counterexamples…

To make the “impossible” at home, following the instructions below, we need only a working Python environment with NumPy (pip install numpy) and its random-number generator. For the sake of reproducibility, I am going to initialize it with seed 0. Then run in Python:

import numpy as np  # let's bring up NumPy

rng = np.random.default_rng(seed=0)  # get a random-number generator

# Magic happens here...
number = rng.integers(
    low=0,
    high=np.iinfo(np.uint64).max,
    dtype=np.uint64,
    endpoint=True,
)

print(number)
# ...

The above code prints on my computer 11749869230777074271. Behold! The probability of observing precisely this number in one draw is 2^-64 ≈ 5 × 10^-20… And yet here it is 😁

Cover image is generated with ChatGPT; prompt and selection by RB.