In a hospital where babies are being born and put into separate lines, do any of these lines of boys and girls seem less likely than the others?:

BBBGGG

GGGGGG

BGGBGB

Intuitively it would appear that the first one seems less likely and certainly the second one is very unlikely. The third one seems as expected as it appears random. But the truth is, all of these events are equally likely.

It is true that it’s more unlikely to have 6 girls in one line than 3. But since every baby’s gender is independent of one another, each line represents 1 possibility in the sample space of all possibilities. Therefore, each specific order is equally likely.

As pointed out in the book Thinking, Fast and Slow, it’s hard to see it that way, even if you know it’s a fact. The easiest thing for our mind to do is to feel there is something non-random about the second line. That there is some orderly intervention that caused the occurrence, relative to the third line.

But there isn’t. And it would be wrong of us to assume so. The question is, where else do we make this mistake? Perhaps in judging other’s people work as good or bad due to a streak? Perhaps judging our own similarly?

The point is, we are not intuitively good at understanding the separation of randomness and order. And we have to be careful in assuming that we always do understand it.