Poll: When is something "statistically impossible"?

This thread piqued my curiosity, so here's the question:

When it is not taxed !

Never.

Unless that choice is expressed up there with the gobbledygook (sp?)

I think this was discussed before, but something can have a probability of 0, and still happen. For example, the probability pi is chosen if picking a random real number between 3 and 4.

By the way, I think 1 in 710 should have been an option, for certain experts of Easy Street Sports, in reference to this dispute.

Actually it is not just p = 0. If the probability of an event is an infinitesimal then, for all practical purposes, the probability is equal to zero.

I would consider an event a "statistical impossibility" if the probability of it ever occurring, i.e. over the appropriate number of trials to cover the entire possible timeframe, in all possible permutations, accounting for both systemic and random factors, is substantially below a set plausibility threshold.

E.g., if there's ~100 poker hands per player per day, for 100 million players, over 365*200 (poker has been popular for a century and will last at least another) days, the event would need to have a less than P.critical probability of occurring in all hands of poker that have ever been and will ever be played, estimated here around 7e14 (for multiple player games).

P.critical can be arbitrary, like 1e-3, 1e-4, 1e-6, what matters in making an event a statistical impossibility, in my view, is that it should be unlikely to be encountered in all trials that have ever and will ever occur.

Systemic factors have to be included, e.g. the probability of each of 4 players in a 4-player game being dealt a royal flush is a combination of the random probability and the probability of an unshuffled deck being used.

Quote: Wizard

I think this was discussed before, but something can have a probability of 0, and still happen. For example, the probability pi is chosen if picking a random real number between 3 and 4. ...

Taking this a little off on a tangent, here is a question for those of you who understand the math better than I do.

Suppose that you did indeed have a randomly-chosen real number between 3 and 4. How would you determine whether it was exactly equal to pi? Allowing that the randomly-chosen number was irrational, would you compare/subtract the two numbers digit by digit? I can see how you might determine that it was not equal to pi, but would it take forever to determine that they were exactly equal? Sounds like a probability of zero that I could finish that task.


Back on topic: I might use the expressions "statistically implausible" or "statistically irrelevant", but I think I avoid "impossible."

If you chose anything other than p=0, then everyday you witness multiple 'statistically impossible' events occurring. I just dealt 2 pai gow hands. The odds of those 2 hands being dealt, before I dealt them, in that sequence, were less than one in a trillion. I watched a hockey game last night. There were exactly seven goals scored at 2:24 and 5:54 of the first period, 11:11 and 17:35 of the second period, 1:59 and 4:44 of the 3rd period, and 2:01 of overtime. The odds of these exact times for goals is less than 1 in a trillion. Someone has suggested that the Pittsburgh Pirates will make the post season this year. The odds of that happening are less than one in a trillion.

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