Hare's theory predicts that there would need to be a cold snap at just the right time, and lo and behold there was. Probability isn't an issue if the only reason you are considering the probability is because the event already happened. Indeed the low probability of such an event transpiring goes a long way towards explaining why the discovery was not made earlier.

Root-Bernstein's theory makes no such testable predictions, and it solves the issue of an incomplete record on September 3rd with incomplete or inaccurate records elsewhere. It seems to me extremely plausible that fleming did not record the results of a botched, uncontrolled experiment but still recognized it as an indicator of something interesting that warranted follow-up. If I were in his position I would preserve the random dish for comparison to the more rigorous follow up experiment. I certainly don't put any stock into the argument that if the story had gone as Root-Bernstein describes it would have been too circuitous for scientific publishing, if anything it would be much more harmonious with standard scientific writing than the chance observation story.

Yeah, I don't see the huge improbability here.

Given that we know that:

- Fleming lived next door to an unsecure mycology lab.

- The temperature during the time period was low enough that if Fleming had left a contaminated culture unattended and non-incubated, he would have had a very high chance of getting the results he became famous for...

Well, given that the probability of discovering penicillin in those conditions is pretty high (say, if he forgot/neglected to incubate one out twenty batches, a 5% chance), and the prior probability of discovering penicillin any other way is extremely low (otherwise other scientists would have found it), bayesian calculus says the stroke of luck hypothesis is probably correct.

> I would preserve the random dish for comparison to the more rigorous follow up experiment

This would also explain why the dish was treated with formaldehyde for preservation, and why the dish still exists today.