> Doesn’t change the fact that each coin toss is still 50/50.

That assumes a fair coin. The fact is you don't know what the odds were of getting heads or tails for that particular coin, all you know is that you got 3/4 heads. And in this analogy, a few hundred coins have every been made, in maybe a dozen styles, none of which have been fair, so you have no good reason to believe that this particular coin should have 50/50 odds of landing heads up.

The original discussion was about acceptable mortality rate. Artemis's target is 1 in 30, which is better than the empirically observed mortality rate of the actual Apollo missions. The mortality rate is a target. And if that target is an improvement over the actual outcome of the Apollo missions, I think it's difficult to say that the target is weaker than Apollo's, which was the claim up the thread that I was responding to.

The public doesn't care if Apollo had a theoretical risk rate lower or higher than 1/12, what they saw was that 1/12 missions resulted in the death of the crew. The NASA administrator explaining that their estimated risk was only 1/1000 doesn't change the real-world perception or outcome.