@JJJ. You don't get the joke. The dice-roll is not related to the event. It is related to the truth statement about the event. The joke is that the frequentist notes that the probability of two sixes is less than 5%, and hence concludes that the truth statement yielded "TRUE" with more than 95% certainty, and hence the neutrino device must have predicted "Sun exploded"
The error, mathematically, is that the error introduced by the two dice dwarfs the likelihood of the event that the truth statement is originally about. So the machine yielding the value "YES" is more likely due to the error introduced by the dice than because the event actually took place.
The XKCD comic is making a point that given a random variable X with error Y, just because Y < 5% (or any d%) and the random variable yields x, does not mean that the random variable is x with a high or even meaningful confidence. If the error margin is large compared with the variable itself, no meaningful statement can be made until large numbers of readings have been taken place to drive down the standard error of the computation in order to even begin to make meaningful statements about X.
This is a commentary by the author of XKCD about how bad people are at these kinds of statistics which occasionally crop up in some important situations. If the likelihood that you have breast cancer is small, and the error on the screening is randomly distributed and larger than that value, then just because you've fallen into the category of "machine says you have cancer" doesn't mean you have cancer. It doesn't even mean you're LIKELY to have cancer. It just means that more tests need to be carried out.