austin_dern (austin_dern) wrote,

Well, I rolled the dice feeling cold as ice

[ Late, yes, for the same incredibly happy reasons. ]

The wonderful thing about probability is that every person, no matter his or her professional standing or social circles, has an intuitive understanding of it, and that understanding is absolutely wrong. The intuitive feeling could not be more wrong if it were designed to confuse everyone. Even the simplest questions lead to incorrect answers, to people yelling at one another over the number of ways each answer is incorrect, and in extreme cases the breaking of tectonic plates. Those may have been coincidental, but the probability of it is impossible to get straight.

Still, probability is one of the most practical fields of mathematics, useful as it is for handling questions regarding how to play very basic yet unrealistic game shows, understanding the quirky family-planning laws of unnamed small nations, or determining how many of a set of five vacuum tubes are broken at any moment. They also let one know how many people need to be in a room before someone has a birthday (one), or how many birthdays have people (366).

Consider: a person you had never met before mentions she has two children, and one of them -- a girl -- enters. What is the chance that the other is a boy? Most people will instinctively answer one-half, considering only the two name-brand genders sold in any considerable amount since 1878. A few, suspecting a trick, have a nagging feeling the correct answer should be one-third, and so answer two-thirds because they got this problem wrong the last time. When the other child does finally enter, having finished working on a similar problem involving three doors, two goats, and a car, this problematic and probabilistic child is revealed to be a giraffe, which has a roughly one in five chance of happening in any group of more than 23 or in a two-giraffe family.

Probability was discovered in the 1260s by the philosopher Francis Or Roger Bacon, and then lost again for centuries, with his manuscript not being discovered until about two hundred years from now. It will be behind the breakfront. The work was recreated by Johann Bernoulli, unless I mean Jacob Bernoulli, which would be the other Jacob Bernoulli, whose name was Nicholaus. But thanks to this work we have a precise understanding of what we don't know, and there are four chances in nine that we don't even know that, which puts us ahead of the curve.

Calculating the probability of something happening is simple: first, identify all the ways in which that thing can happen. Then identify all the ways in which anything at all can happen. This may require extra paper, and don't think you can skip listing the things you never imagined happening. They might just turn out anyway and you don't want to be caught by surprise. Also don't forget to list all the things which turn out like you wanted to see happen even when they turn out just too perfect, because these are good for extra credit.

Next, add up all these things which you're curious about happening or that you don't want to have happen, adding to the total one for every event that's just as likely to happen as any other event is, two for every event that's twice as likely to happen as any other is, one-half for the things half as likely to happen, and square root of two for everything one-over-the-square-root-of-two likely to happen. This should get you two numbers, one of them at least as big as the other.

Divide the larger number by the smaller, and you will find that this was done the wrong way around. It should be dividing the smaller number by the larger, and this gives you the probability of the event you were interested in happening. That may not mean it actually does happen that way, but at least you gave it an honest try. If you do not have a larger number, then write one down using bigger numerals, and roll the dice until you score a nine or above, which can be done most efficiently by using at least ten dice.

Trivia: Karl Pearson demonstrated the runs in roulette at Monte Carlo in July 1892 did not match those expected from pure chance, and estimated the odds against such an outcome being a random fluctuation of honest tables as 1000 million to one against. Source: Randomness, Deborah J Bennett.

Currently Reading: Three To Zero: The Story Of The Birth And Death Of The World Journal Tribune, Joseph Sage.


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