A probability mistake

December 13, 2016 § Leave a comment

Game 1

There is a box of marbles. You know, marbles like this.


If 1000 such marbles are in a jar, 998 of them white, and 2 of them red. Now you dip your hand into these smooth marbles and take out one.

What are the chances that it is red?

Yes, 2/1000, or 0.2%.

Fair game.

Game 2

Now, let’s do something else. There are 1,000 students who apply for a very selective high-mathematics program. The program can only have 2 students this year. Yeah, it’s hyper-mega-selective.

For any random student, the chances of getting selected are – 2/1000. Right?


Because all students are not alike. Unlike the marbles. A student who comes from a a well educated family, say, a doctor’s son has much better chances than 0.2%, and the son of a bicycle repair mechanic has much worse chances than 0.2%. And also, both these odds are  not strictly computable. The odds would be the same if the students were exact clones both in terms of DNA and Environmental factors – and this is never the case with the complexity life offers us.

This might seem simple and trivial, but we make this basic mistake many times. Even Elon Musk. See if you can see the flaw in his argument.

If you didn’t, sample this. There are more than 7 Billion people on the earth right now. Almost all of them dream. A dream is indistinguishable from reality. So, the chance that you are reading this blog in a dream is 1/7 Billion? Or, around 56 Billion people have been known to exist till now, so the chances could be 1/56 Billion that this is real? Or what about animals? Do they dream? Micro-organisms? Aliens?

Or let’s take this even further. You are in the room with say, 200 novels. All these novels have different characters. Let’s say there are 1,000 characters in the same room as you are. Now, are the chances you being a fictional character 1 in 1,000? What about all novels available? What about all novels which ever existed? What about all oral stories AND novels which ever existed?

It’s fun and stimulating intellectual exercise to think that whatever we see is a simulation. I definitely recommend it for the next party. But it is downright dangerous to not understand  how probability works in making important decisions. Most of the times, it is almost impossible to judge probability in real-life situations. But what’s more, you don’t even need to judge. For example, you don’t need to know the exact chances of accident due to drunken driving, to know that you should not do it.

If you are interested in more regarding these, I strongly suggest reading books by Nassim Nicholas Taleb – which have a lot of stories about how massively impactful decisions went wrong, because people did not think about the odds clearly.


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