People have had a hard time getting their head around that idea for millennia.

亚里士多德也掺合上了。

Maybe I'm getting a big head. I'm not sure.

也许我脑袋大了。 我不确定。

So are we getting head faked?

那么我们是不是被骗了？

That's the same thing as getting 4 heads, so that's like that.

这与获得 4 个正面相同，所以就是这样。

And my hair started singeing just barely even getting my head in the door.

我的头刚进门就开始烧焦了。

That was fair: we all know there’s an equal chance of getting heads and tails.

这是公平的：我们都知道正面和反面的机会均等。

The chances of getting either two heads or two tails in a row are 50% times 50%— or 25%.

连续出现两个正面或两个反面的几率是 50% 乘以 50%，即 25%。

The probability of getting 1 head we figured out was 5 over 32.

我们计算出获得 1 个正面的概率是 5 比 32。

And the probability of getting 2 tails should be the same thing as the probability of getting 2 heads.

得到 2 个反面的概率应该和得到 2 个正面的概率是一样的。

And if any time you thought I was getting a big head, you made sure you put me right back in my place.

而当你们觉得我有些自以为是的时候，你们也一定会让我回到正轨。

These are all mathematical tools for getting our heads around numbers.

这些都是让我们了解数字的数学工具。

In very general terms, it's getting your head around data.

用非常笼统的术语来说，它让您了解数据。

And once again, notice, the probability of getting 4 heads is the same thing as the probability of getting exactly 1 head.

再次注意，获得 4 个正面的概率与恰好获得 1 个正面的概率是一样的。

And the probability of getting 2 tails should really be the same thing as the probability of getting 2 heads.

得到 2 个反面的概率实际上应该和得到 2 个正面的概率是一样的。

And that made sense because the probability of getting 3 heads is the same thing as a probability of getting 2 tails.

这是有道理的，因为获得 3 个正面的概率与获得 2 个反面的概率是一回事。

And what we essentially did in the last video when we said, OK, what was the probability of getting exactly two heads?

我们在上一个视频中基本上做了什么， 我们说， 好吧，恰好有两个正面的概率是多少？

If one of these was-- you can't have a 60% probability of getting a heads and then a 60% probability of getting a tails as well.

如果其中之一是——你不可能有 60% 的概率获得正面，然后也有 60% 的概率获得反面。

And for me this is something that I always had a lot of trouble getting my head around, and that's really because it's a byproduct of what it's called.

对我来说，这是我总是很难理解的事情，那真的是因为它是所谓的副产品。