And if we just look through them all, we can count up how many pairs have a given sum.

如逐一查看它，就可以统计出有多少对数的和等于给定的值。

Other images that can come to mind, to think of all the distinct pairs that have a given sum?

想到所有和为给定值的不同数对，还能联想到哪些像？

Looking at a unit circle, the tangent of any given angle is the height of this little triangle divided by its width.

观察单位圆，任何给定角度的正切值是这个小三角形的高度除以它的宽度。

If you actually then said, oh, this is a binomial distribution, so the probability that our random variable equals some given value, k.

如你实， 这是一个二项分布，所以的随机变量等于某个给定值k的概率。

It can only happen if the frequency of the light rays is equal to or greater than a given value — known as the threshold frequency — of the metal.

只有当光线的频率等于或大于金属的给定值（称为阈值频率）时，才会发生这种情况。

In normal, finite settings, like rolling a die or drawing a card, the probability that a random value falls into a given collection of possibilities is simply the sum of the probabilities of being any one of them.

在正常的有限设置中， 比如掷骰子或抽牌，随机值落入给定可能性集合中的概率就是这些可能性各自概率的总和。