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The United States Supreme Court found that the "extreme facts" of the case raised the probability of bias to an unconstitutional level.
VOA: special.2009.06.12
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So the probability of having an electron at the nucleus in terms of probability per volume is very, very high.
在单位体积内发现,一个电子的概率非常非常大。
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The mathematical theory of probability was unknown until that time and you can see that insurance suddenly made an appearance at that time.
在那之前,概率的数学理论,是不存在的,而随着概率论的出现,保险业也突然出现了
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The IPCC report said that the probability of the mass of ice "disappearing by the year 2035 and perhaps sooner is very high."
VOA: standard.2010.01.23
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s And if we go ahead and superimpose the 3 s on top of the 3 p, you can see that the 3 s actually has some bit of probability density that gets even closer to the nucleus than the 3 p did.
如果我们继续将,重叠到3p上面，你们会看到3s事实上,有一点概率密度,距离原子核更近,比3p轨道。
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"If a woman gets breast cancer in the developing world, they has a much higher probability of dying than a woman who gets breast cancer in the developed world."
VOA: standard.2010.02.02
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In fact, you'll find the probability of this happening 3% is only about 3 percent, of it happening just by accident.
实际上你会发现,出现这种情况的概率是，所以说他们的实验结果完全是偶然的。
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So the probability is 0 of the other guy choosing Left is, the same as, let's try it again.
同样的如果对手选左的概率是0,那也就是说,重新来
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And this is proportional to the probability of finding an electron.
它和观察的电子云概率,成正比关系。
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I think it was the invention of probability theory that really started it and that's why I think theory is very important in finance.
我认为是概率论的诞生,真正促生了保险业,那也是为什么,我认为理论对于金融来说非常重要
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You can see how they moved from that definition of probability to the current definition.
所以你可以清楚地了解到,概率是如何由那个定义,转变为今天的定义的
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Ian Hacking, who wrote a history of probability theory, searched through world literature for any reference to a probability and could find none anywhere before 1600.
伊恩·哈金为概率论追根溯源,他查遍世界所有关于概率的文献,发现无法追溯到十七世纪以前
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We're also going to recognize, however, that insurance got a slow start because-- I believe it is because-- people could not understand the concept of probability.
不管怎么说,我们得承认,保险起步缓慢,因为...,我相信是因为...,人们无法理解概率的概念
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So, let's go ahead and think about drawing what that would look like in terms of the radial probability distribution.
让我们来想一想如果把它的,径向概率分布画出来是怎么样的。
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So, once we figure out what our probability of backscattering is, we'll just raise that to the 1/2, and we'll multiply that by 12 . 20 centimeters.
所以一旦我们,知道了散射概率，我们开根号。
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And in principle, I could redo this calculation for every single possible probability you could think of.
并且理论上,对于每一个可能的概率对,我们都可以进行预期收益计算
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One of the first principles of probability theory is called the multiplication rule.
概率论的最基本的原则,有一条叫乘法原理
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One of the first principles of probability is the idea of independence.
概率论中最基本的一个原则,就是独立性的概念
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And when we do that we can see this curve, this probability curve, where we have a maximum probability of finding the electron this far away from the nucleus.
当我们这样做时，我们可以看到这个曲线，这个概率分布曲线，这里有发现,电子的最大概率。
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So we can see if we look at the probability density plot, we can see there's a place where the probability density of is actually going to be zero.
就能看到,有些地方，找到一个电子的,概率密度,我们可以考虑。
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And when we take the wave function and square it, that's going to be equal to the probability density of finding an electron at some point in your atom.
当我们把波函数平方时，就等于在某处,找到一个电子的概率密度。
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We can not do that with quantum mechanics, the more true picture is the best we can get to is talk about what the probability is of finding the electron at any given nucleus.
在量子力学里我们不这样做，我们能得到的更加真实的图像,是关于在某处,找到电子的概率。
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But what we're saying is there's a node here, so that there's no probability of finding an electron between those two points.
但我们说在节点这里，这两点是,不可能发现电子的。
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But they're accountable and we can list all possible values when they're discrete and form a probability weighted average of the outcomes.
但随机变量是离散的话,我们可以把所有的可能值列出来,然后算出加权平均值
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If you follow through from the independent theory, there's one of the basic relations in probability theory-- it's called the binomial distribution.
如果继续往下看,在概率论里有一个基本的概念,叫做二项分布
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So, let's actually compare the radial probability distribution of p orbitals to what we've already looked at, which are s orbitals, and we'll find that we can get some information out of comparing these graphs.
让我们来比较一下ｐ轨道,和我们看过的,ｓ轨道的径向概率分布，我们发现我们可以通过,比较这些图得到一些信息。
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Anywhere where that's the case we're going to have no probability density of finding an electron.
这时面内任何地方,找到电子的概率密度都是零。
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The answer is, in fact, there is zero, absolutely zero probability of finding a electron here.
实际上它在这里是为零的，在这里找到电子的概率严格等于零。
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So because we're feeling a stronger attractive force from the nucleus, we're actually pulling that electron in closer, which means that the probability squared of where the electron is going to be is actually a smaller radius.
因为我们能感到来自原子核,的更强的吸引力，我们实际上会将电子拉的更近，那意味着电子运动的,概率半径是,事实上是一个更小的半径。
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The other thing that we looked at, which I want to stress again and I'll stress it as many times as I can fit it into lecture, because this is something that confuses students when they're trying to identify, for example, different nodes or areas of no probability.
另外一个我们要考虑的事情，我想再强调一次,而且我以后会在课上强调很多次，因为它很容易让人混淆,这就是当你们在确认，节点或者零概率点时候。
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