Saturday, June 23, 2012

A quick lesson on calculating probability

Something I posted over at ThreeSources, to clarify a discussion about one molecule in each drop, and the probability of getting at least one from two drops:
The total probability is actually not the sum of the individual events' probabilities. If the chance is 50%, then the odds of one in two drops is 75%. There's still a 25% chance of two drops having no molecules in either. With three drops, it's still only an 87.5% chance of having at least one molecule. The easy way to think about it: what's the possibility of all the events happening? Subtract that from 1, and that's the probability of at least one event happening.
In various "dungeons and dragons" games I've played over the years, weapons can have a couple of different effects, each with its own probability. Let's say one has a 40% chance to hit with one spell, and 30% with another. The probability of both occurring together is easy: 12%. The probability of at least one is not 40%+30%, but rather 58%: 1 - (1-.4)(1-.3). The odds that neither will happen is 42%.

By these formulas, you can see that 100 events of 99% probability each will have a close to but still not quite 100% (1 minus 10^-200) that at least one will happen. The odds that all will happen is about 36%. Probabilities aren't really hard, yet many Americans don't bother to learn a little bit about them, instead going their entire lives swallowing whatever's thrown at them. I wasn't surprised that some idiot news reporter gushed about a "Three billion to one" event at a roulette wheel, mentioning an alleged "professional poker player" (who is bound to know a thing or two about odds) who just didn't simply dismiss the display as inaccurate, but said the wheel was rigged!

People just don't apply simple sense. There would have been a hell of a lot more "jumping up and down" if the same number had really come up that many times, but it would have never come to that. The same number hitting more than a couple of times in a row is improbable enough that after a few runs, the floor manager would have shut down the wheel as malfunctioning.


Blogger johngalt said...

... and with four drops it's a 93.75% chance of having one molecule. I call that an "almost certainty" don't you? If there was a 100% chance I'd be obliged to call it an absolute certainty.

P.S. You forgot to cross-link to the ThreeSources post! ;)

Monday, June 25, 2012 3:22:00 PM  
Blogger Perry Eidelbus said...

Oh, I didn't put in the link? Thanks for that, these days I'm rushing too much to throw things out.

"Certainty" all depends on what you're looking for. If you're trying to get a single molecule, get 10 drops. Now if it's certain things I approve at work that deal with options, I've had to explain my denials to more than a few people. Even if a particular price movement has a 1 in a thousand chance, it would be just my luck to have it happen.

Sunday, July 01, 2012 11:55:00 AM  

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