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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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We can talk about the wave function squared, the probability density, or we can talk about the radial probability distribution.
我们可以讨论它,波函数的平方，概率密度，或者可以考虑它的径向概率分布。
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It takes on the value 1 with the probability of 20% and the value of 0 with the probability of 80%.
等于1的概率是20%,等于0的概率是80%
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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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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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And when we define that as r being equal to zero, essentially we're multiplying the probability density by zero.
当我们定义ｒ等于０处，事实上是把概率密度乘以０．
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And the trend always is that the probability gets smaller with each of the peaks as you're drawing them.
当你画它们的时候,整体趋势总是每个峰概率越来越小。
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So the right question to ask is, what's the probability, not that June had 48 babies, but that at least one of the 12 months had 48 babies.
所以正确的问题是，不是去看这个6月,有48个宝宝出生，而是去看至少有一个月的出生人数。
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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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it's going to be: 1 minus the probability they'll choose Right times 1, plus the probability that they choose Right times 4.
方程是,1减对手选右的概率再乘以1,加上对手选右的概率乘以4
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That says that if you have independent probabilities, then the probability of two events is equal to the product of their probabilities.
意思是,几个相互独立的事件,其中两个事件同时发生的概率,等于他们分别发生的概率的乘积
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But still, when we're talking about the radial probability distribution, what we actually want to think about is what's the probability of finding the electron in that shell?
但当我们讲到径向概率分布时,我们想做的是考虑，在某一个壳层里,找到电子的概率,就把它想成是蛋壳？
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Ever since this was first proposed, there has never been any observations that do not coincide with the idea, that did not match the fact that the probability density is equal to the wave function squared.
从未有，任何观测，与它相抵触,从没有过，波函数的平方不等于,概率密度的情况，关于马克思，波恩。
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So, if I kind of circle where the probability gets somewhat substantial here, you can see we're much closer to the nucleus at the s orbital than we are for the p, then when we are for the d.
我把概率,很大的地方圈出来，你们可以看到在ｓ轨道上,比ｐ轨道更接近原子核，最远是ｄ轨道。
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What would be the probability that a married couple would live, both of them, to the time when their children were grown?
一对已婚夫妇双双活到,孩子成年之后的概率是多少呢
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And if we go ahead and square that, then what we get is a probability density, and specifically it's the probability of finding an electron in a certain small defined volume away from the nucleus.
我们得到的是，一个概率密度，它是，在核子周围，某个很小的,特定区域,找到电子的概率,所以它是概率密度。
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And when we're looking at the probability density graphs, it doesn't make a difference, it's okay, It has no meaning for our actual plot there, because we're squaring it, so it doesn't matter whether it's negative or positive, all that matters is the magnitude.
它的概率密度图的时候,两者没什么区别，这是可以的，它对我们画这个图，没有什么意义,因为我们是取平方，所以它的正负，无所谓，只和幅值有关，但当我们说到。
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It uses the binomial distribution to calculate the probability of getting any specific number of accidents.
保险公司就可以用二项分布公式,来计算特定数目事故发生的概率
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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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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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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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