In fact, we could then draw a Bayesian inference.
(1) The probability of any event in a deterministic universe is 1, so P(E|D)=1.
(2) The probability of any event in a non-deterministic universe is unimaginably small; I estimate it at 10-1000 at best, so P(E|~D)<10-1000.
(3) We cannot tell whether the universe we live in is deterministic or non-deterministic, therefore we can assign an initial estimate of 0.5 for the probability that the universe is deterministic. P(D)=P(~D)=0.5.
(4) According to Bayes' Theorem, P(D|E)=P(E|D)P(D)/P(E)
(5) We can estimate the probability of any event as the average of its probability in a deterministic and a non-deterministic universe, which gives the result that the probability of any event is (0.5+5x10-1001), insignificantly different from 0.5.
(6) Substituting into Bayes' Theorem, we find that P(D|E), the probability that we live in a deterministic universe given that any event has actually taken place, is (1x0.5/0.5) = 1.
(7) Therefore, the fact that any event has taken place demonstrates that we live in a deterministic universe.
And please don't criticise me for posting that. As you can see, I didn't have any choice.
Dave