The title pretty much says it all. Probability can me measured; sometimes the results can be applied to reality/history. What is the very most verifiably improbable occurrence believably recorded?

Do you mean where the event’s likelihood had been calculated *before* it occurred? Or, a retrospective estimate as in, “Wow, the odds of that meteorite hitting him right on the head are, like, a billion to one!”? Or, less facetiously as in, “scientists estimated that the chance of lightning striking the same (unlucky?) man within one week were less than one in a billion”?

that life would evolve on earth in the way it has

I have some problems with this question:

(1) How do you define an “event”?

(2) An event can be highly improbable, yet totally unremarkable. For example, if you shuffle a deck of cards, *any particular* arrangement of the deck that results is very, very improbable, but most of them are quite unremarkable.

(3) I’m not sure you can really say that probability can be “measured”—if so, *how*? Probability can be *calculated*, from certain initial assumptions, but how do you know how well those assumptions correspond to “reality”?

The only way to have even a remotely sensible interpretation of the OP is if, as suggested above, the event was defined and its probability calculated (or estimated) before it actually does or doesn’t happen. (And even then, you have to define the “event window”, so if it doesn’t happen, you will know when to conclude that it didn’t happen.)

Once an event does (or doesn’t) happen, its probability collapses to exactly 1 or 0. For example, once you’ve flipped a coin and it has already landed either head or tail, then the “probability” of it landing “head” is exactly 1 or 0 (depending on how it landed), no longer 0.5 – Basically, it becomes meaningless to talk of probability of an event after-the-fact.

Probabilities are computed ahead-of-time in basically two ways:

Either by enumerating all the possible outcomes and counting various combinations of those (this is the “simple-minded approach” typically envisioned in your math books), or more realistically by looking at real-life history of past events and extrapolating to future events – for example, predicting probability that it will rain, by looking at a history of days that had similar weather indicators, and noting how many of those times it rained.

ETA: As for the OP’s question, I’d say that getting a job interview in response to an application is a particularly low-probability event these days.

Probably detecting a neutrino.

Something like 1 in a trillion are detected.

There are wonderful coincidences in the world…like the guy who’s house was hit by cannon fire during the exchange at Fort Sumter later being the owner of Appomattox Court House, or various people who have been hit any number of times by lightning, or someone who has won the lottery several times, etc.

I’m sure there is some record, somewhere, of someone winning an absurd number of hands of poker in a row… I think those may be the kinds of events the OP had in mind…

That, I, me, moi, is here alive and thinking.

Given an arrangement of every particle and the energy that existed at the instant of the big bang’s initiation, what are the odds that those things would rearrange themselves over time to the precise arrangement we have today?

Right. The lowest-probability event that has ever happened is the probability, at the moment of the start of the universe, that everything would play out exactly as it has done up to the present moment. By definition there can’t be an event more unlikely than that which has happened.

If you want an answer narrower than that then we’d need to define “event” more narrowly.

Well shucks, I guess it isn’t a very good question after all. I meant in retrospect, but as has been pointed out, that doesn’t really mean what I want it to mean. I was thinking about how people make decisions based on the odds of things happening. Some things are quite likely and that’s what people bet on. But on the low end, I was just wondering how low of a probability I should assign for the ‘floor’. I suppose the whole universe turning out like it did is the correct answer, which 1) leaves open the question of what the odds of that happening actually are and 2) makes this look kind of like a dumb question. Sorry, that happens to curious minds sometimes.

No,

It is not a dumb question. I think this thread has all kinds of interesting possibilities, some statistcally/scientifically meaningful (like the neutrinos) and some not so much but still interesting/humorous (like the cannonball story).

It was Wilmer Mclean and it was the first ballte of Bull Run that his house was hit leading him to move to Appomattox Court House. His house was where Lee surrenderd to Grant. The town was named Appomattox Court House. The surrender was in a private house not a court house.

Although my answer is related to the above, it is not the same. The big bang was an apparently spontaneous event at which entropy was essentially 0. Since entropy, on average, always increases, this is an event of extremely low probability. But in the infinitude of time (my take on the universe) everything that can happen will.

but how many neutrinos are there? The chances of detecting a particular pre-defined neutrino might be very slim, but if there are a million trillion neutrinos then detecting one if you wanted to would be quite possible I imagine.

As to the OP, I think the main issue is your contention that probability can be measured, known, calculated somehow. I think that for most real-world events, that’s not actually the case. For instance, I don’t think that one can meaningfully speak about the probability of Israel bombing Iran in the coming month, neither beforehand (ie now) or after the fact.

Take a look at the so-called D-Day crossword puzzle coincidences.

The following were D-Day related code words which appeared as answers

in the London Daliy Telegraph shortly before D-Day (planned for early June):

Utah (appeared May 2-- codeword for assault target beach)

Omaha (appeared May 22-- codeword for assault target beach)

Overlord (appeared May 27-- codeword for entire operation)

Mulberry (appeared May 30-- codeword for prefab artificial harbors)

Neptune (appeared June 1-- codeword for naval aspect of operation)

The code words for the other three beaches-- Gold, juno and Sword

also appeared in LDT crosswords but I cannot find dates for them.

Odds against such a coincidence against must be 10^-20 or worse.

One explanation suggested was that the crossword author, a teacher,

indirectly obtained the words from students who had been sociliazing

with military personnel who dropped the words in conversation. One

wonders how the Allies could have ever succeded in anything if security

could be so casually breached.

There are so many neutrinos that the odds some will be detected

with the right equipment are 100%.

1000s of them pass through our bodies every second.

I agree that you have to be really careful with this question because the probabilities have to be calculated first and the assumptions have to be correct.

One possible answer is multi-million dollar lottery winners. We all know playing the lottery expecting to win is a fool’s game yet a few people do win. It would seem that the odds of someone winning the lottery more than once would be astronomical and it is if you pick the person ahead of time. However, among all lottery winners, it is an almost certainty that one or more of them will win again if they keep playing regularly for a few years. Just as predicted, there have been a few people people that have won the lottery twice but there is only one [Joan Ginther of Texas who has one multi-million dollar payouts four times so far.](Joan Ginther)

“Mathematicians say the chances are as slim as 1 in 18 septillion – that’s 18 and 24 zeros.” says the article. There is a problem with that calculation. That may be true if you calculated it for a given person before she started playing at all and make the assumption that the lottery is completely random but we don’t know that is really the case. Joan Ginther is also a retired math professor so she understands the odds just fine and may have come up with a way to beat the lottery. She plays scratch tickets mostly and some of those games have been beaten in several states because they aren’t truly random.