In other news, probabilities again used to prove whatever conclusions we were planning to present anyway.

It is time to stop the show, probabilities cannot prove specifics. Aka they cannot prove that the coin I hold is fair or not. We can only get trends for big populations.

There is only one way to prove if a coin is fair. Measure the actual thing that matters. In this case mass distribution. And if the measurement is inaccurate, then count atoms. One by one.