[stetrain]

> If I toss a coin four times and it comes up heads three and tails once, it doesn’t mean that there’s a 75% chance that this coin lands heads up.

No, but it means that to ensure that I do better on my next set of coin tosses I need to beat 3 in 4, not 1 in 2.

[d1sxeyes]

But you doing better is independent of the risk involved. The chances of you getting 3/4 heads or better is around 31%, so theres ~69% chance you’ll do worse next time round. Doesn’t change the fact that each coin toss is still 50/50.

[jjk166]

> 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.

[d1sxeyes]

But the idea we're exploring is that the coin is fair (i.e. the 1/1000 estimate is correct, and the Apollo missions were unlucky).

[jjk166]

And it may be, but the important thing is we don't have priors that lead us to expect it to be fair.

We are not dealing with the tautologically true statement that we are assuming the 1/1000 estimate is correct and thus the odds are 1/1000 no matter what we measure. We are dealing with whether or not we can safely reject the hypothesis that the true odds are 1/1000 based on the actual observation of 1/12.

Billions of coins have been minted, and flipped a countless number of times, and we can do the physical analysis of coins such that we know the odds of a coin not being fair, without deliberate intervention to make them such, are astronomically low. As such no one is going to reject the hypothesis that a coin is fair based off of a small number of coin tosses. Hell even if you got 10 heads in a row, while the odds of that sequence is 1 in 1024, we would probably conclude it was luck rather than that the coin was flawed.

For spaceships on the other hand, those priors don't exist. We need to look at just the data from this particular test. The odds of a 1/1000 event occurring in the first 12 attempts is 1 in 84. For rejecting the hypothesis that a mass produced coin is fair, those odds aren't bad; but for rejecting the null hypothesis that the apollo capsules were just unlucky it's way over the reasonable threshold.

[stetrain]

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.

[d1sxeyes]

I think we're approaching this from different angles. 1 in 30 is better than the observed rate, but worse than the estimated rate.

FWIW, the 1/12 is also actually off, the long-term mortality rate for Apollo astronauts is high.

But so is the 1/1000, Nasa's own estimates were so bad that they decided it was bad optics to keep doing them - https://ntrs.nasa.gov/api/citations/20190002249/downloads/20...