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We can actually have any radius, but some radii just have much, much smaller probabilities of actually being significant or not.
非常非常小，以至于,无关紧要,我们今天。
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These are called population measures because they refer to the whole population of possible outcomes and they measure the probabilities.
这些是用来度量总体的变量,因为他们对应的是总体中所有的结果,度量的是所有事件的概率
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What probabilities are associated with thinking it's twice as likely they're going to choose Left than Right?
那么在选左是选右的可能性的二倍时,选择每个策略的概率是多少呢
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Because if we think about wave behavior of electrons and we're forming bonds, then what we have to do is have constructive interference of 2 different electrons, right, to form a bond, we want to and together those probabilities.
如果我们考虑,电子的波动行为,并且，我们要成键的话,我们要,把，这些概率，加在一起,如果。
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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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There was an intellectual leap that occurred in the seventeenth century and it became very fashionable to talk in terms of probabilities.
也就是说,十七世纪中,诞生了一次智慧的飞跃,用概率来表述成了件很时髦的事
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It turns out that the probabilities of scoring here are as follows, 63.6, 94.4, 89.3, and 43.7.
研究的结果,概率分布如下,63.6 94.4 89.3 和 43.7
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If you offer life insurance, you have life tables which give you probabilities of dying at various ages, but that's for the general population.
如果你提供人寿险,你会找张寿命表,告诉你各个年龄段的死亡率,但那是针对普通人群的
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London insurance companies would because the whole concept of insurance is pooling of independent probabilities.
伦敦的保险公司之所以开展火险,是因为整个保险理念,就是将独立事件发生的风险汇聚起来
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In order to compute using this formula you have to know the true probabilities.
使用这些公式之前,必须知道真实的概率值是多少
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They don't really take, at an intuitive level, probabilities as objective.
从直觉上来说,他们并不真的认为,概率是客观的
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So what we're going to do is we're going to look at some numbers that are approximately the probabilities of scoring when you kick the penalty kick in different directions.
接下来,我们来用数字表示,在不同角度踢点球射门,能够得分的概率
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It spread throughout the world--the idea of quoting probabilities.
引用概率的这种表述方式很快传遍世界
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So equally likely was probabilities of ? and ?.
这个?与?的可能性是类似的
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It means all probabilities in between.
它包含了所有可能下的概率
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What probabilities are associated with that: .
概率分别是多少
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So things are not... I haven't given you the numbers for the middle but... So you can see that whoever it was who said, you're slightly better off, you score with slightly higher probabilities when you kick to your natural side is exactly right.
所以事情不像是……,我虽然没有给出中路的概率,但是,我们先不管这些数字到底是谁总结的,我们发现我们走运了,当你从自然方向攻门的时候,你进球的概率会稍微提高
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Problem is here, that Player II has a continuum of strategies and trying to draw all possible probabilities over an infinite number of objects on the board is more than my drawing can do. Too hard.
现在问题是,参与人II的策略是连续的,想要把无限可能性的概率,做成图都画在黑板上,是不可能的了
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They have maybe a sense that I can influence events by willing or wishing and if I think that-- if I have kind of a mystical side to me, then probabilities don't have a clear meaning.
他们也许觉得 我可以通过意愿或者许愿,来影响事件的发展,也许...,我说不定有神力相助,如此概率这个概念就有些模棱两可了
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These are probabilities.
这些数值是概率
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The reaction that salespeople would get from women was, you're giving me some probabilities or something, you're asking me to-- it sounds like you're asking me to play in some gambling thing where I win if my husband dies; it doesn't sound right to me.
推销员从女性那里得到的回答是,你跟我讲了一通概率之类的东西,然后劝我...,这听起来似乎是在让我去赌博,如果我丈夫去世了,那我就赢了,这太不对劲了
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So here what we did before was we drew these graphs with probabilities, with beliefs of Player I and the problem here is, previously we had a nice simple graph to draw because there were just two strategies for Player II.
我们之前画了有关概率的图像,图像是在参与人的某个信念下的,但问题是之前参与人II只有两个策略,所以我们能画出那个简单的图像
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