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"We are going to need more taxpayer money up front. I think that another stimulus package is a reasonable probability, given the way things are going,"
VOA: standard.2009.03.10
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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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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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If someone says the probability is .55 or .45, well you know what that means.
如果有人提到概率是0.55或者0.45,你就知道他说的是什么意思了
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Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.
我们的朋友薛定谔告诉我们,如果你用波函数来解决，你就会知道这些概率密度看上去的样子。
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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 on the horizontal axis is my belief, and my belief is essentially the probability that the goalie dives to the right.
横轴表示的是我的信念,我的信念表示,我认为门将扑向右路的概率
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But the reality that we know from our quantum mechanical model, is that we can't know exactly what the radius is, all we can say is what the probability is of the radius being at certain different points.
我们不可能准确的知道,半径是多少，我们只能说，它在不同半径处，的概率是多少，这是,量子力学。
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So, basically what we're saying is if we take any shell that's at some distance away from the nucleus, we can think about what the probability is of finding an electron at that radius, and that's the definition we gave to the radial probability distribution.
本质上我们说的就是,如果我们在距离原子核,某处取一个壳层，我们可以考虑在这个半径处,发现电子的概率，这就是我们给出的,径向概率密度的定义。
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So, he's using intuitive-- he says difficult or easy-- so he says it's difficult, meaning the probability is very low, or easy, meaning that probability is high.
所以他直接进行了描述,他用的是困难和简单两词,他说的困难,意思就是概率很小,他说的简单,意思就是概率很大
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If the probability is zero that means the event can't happen.
如果概率等于0就意味着事件不会发生
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We can graph out what this is where we're graphing the radial probability density as a function of the radius.
我们可以，画出它来,这是径向概率密度,作为半径的一个函数图。
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This is the radial probability distribution formula for an s orbital, which is, of course, dealing with something that's spherically symmetrical.
这个ｓ轨道的,径向概率分布公式，它对于球对称,的情形成立。
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I've learned that with high probability, the error is not in the first part of the program.
我从这一点得到了什么？,我得到的是错误有很大的可能。
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If the probability is 1 in 1,000 that a house burns down and there are 1,000 houses, then the probability that they all burn down is 1/1000 to the 1000th power, which is virtually zero.
如果一栋房子着火的概率是千分之一,然后假设有1000栋房子,那么这一千栋房子全都着火被烧掉的概率,就等于千分之一的一千次方,基本上就是0了
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But we can also think when we're talking about wave function squared, what we're really talking about is the probability density, right, the probability in some volume.
波函数平方,的时候，我们说的，是概率密度，对吧,是在某些体积内的概率，但我们有办法。
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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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Similarly, if we were to look at the radial probability distributions, what we would find is that there's an identical nodal structure.
相似地如果我们看看,径向概率分布,我们会发现有一个完全相同的波节结构。
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There's some probability that it can get very, very close the nucleus, and that probability is actually substantial.
有一定的概率,它能非常非常接近原子核，这个概率是相当大的。
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At first it might be counter-intuitive because we know the probability density at the nucleus is the greatest.
起初我们觉得这和直观感觉很不相符,因为我们知道在原子核,出的概率密度是最高的。
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And so, the radial probability density at the nucleus is going to be zero, even though we know the probability density at the nucleus is very high, that's actually where is the highest.
所以径向概率密度,在核子处等于零，虽然我们知道在，核子处概率密度很大,实际上在这里是最大的，这是因为。
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So what we should expect to see is one radial node, and that is what we see here 3s in the probability density plot.
个节点,这就是我们，在这概率密度图上所看到的,如果我们考虑。
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Conversely, if there was probability 1 that the other guy is going to choose Right, and I choose Up, then I get 0.
相反,如果对手,选择右的概率为1,并且我选的是上,那我的收益为零
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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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So here, what I'd like you to do is identify the correct radial probability distribution plot for a 5 s orbital, and also make sure that it matches up with the right number of radial nodes that you would expect.
这里，你们要辨认,哪个是５ｓ轨道的正确概率分布，并且确保它和你们,预期的节点数相符合。
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This is the probability density map, so we're talking about the square here.
这是它的概率密度图，我们看的是平方。
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If this probability is 0 that the other guy chooses Right, that's the same as saying that the other guy is going to choose Left.
如果对手选右的概率是0,也就是说我认为对手绝对会选左
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But it turns out the probability is only significant within one angstrom.
但概率主要,分布在一个埃范围内。
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If the probability is--Can everyone see this from over there?
如果概率是...大家都能看清黑板吗
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So think about what that means, we're, of course, not talking about this in classical terms, so what it means if we have an electron in the 2 p orbital, it's more likely, the probability is that will be closer to the nucleus than it would be if it were in the 2 s orbital.
想想这意味着什么，我们不是从经典的角度考虑，这意味着如果我们有个电子在2p轨道上，它更有可能比在2s轨道上,更加靠近原子核。
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