How wrong we can be

When it comes to probability, our intuition tends to lead us the wrong way. A lot of the world of probability works in a counter intuitive manner. Because of this a 'gambler's fallacy' works its way into our thought process when trying to predict how certain events will unfold; from the roll of a dice to the lottery.

This is something I plan to talk about a lot over the coming posts but seeing as I'm still burnt out from my silly bourbon drinking last night I'm going to keep this short. What I'll leave you with is one of these cognitive 'illusions' taken from Derren Brown's book 'Tricks of the Mind'. It's paraphrased so apologises for not having the same wit or writing skills as the man himself.

Imagine there's a disease. This disease if contracted will condemn you to certain death. But the chances of you catching it are very slim, 10, 000:1.
There exists a test that can tell you whether or not you have this fatal disease. You go to the doctor to take the test where you are informed that the test will deliver a correct negative or positive 99 percent of the time.
A week later you get the results in the mail and to your horror the result is positive.

What are your chances of having the disease now that you have this information?
99 percent surely? In fact your chances are less then one percent.

Unless you've heard this problem before or have studied statistics the above conclusion is naturally jarring. It doesn't make sense. But with these kind of cognitive mind fucks you can't go on instinct – your intuition. You have to break it down.

First, the chances of you not having the disease are huge – 9,999:1. Now, let's say 1 million people take the test. Only one hundred people will have the disease. Ninety nine will have got a correct positive while just one will have gotten back a false negative. Now, on the other side of the coin 999, 900 will not have the disease but 1 percent will get the false positive (9,999 people)

So are you more likely to be one of the 99 who have the disease or one of the 9999 that don't and received a false positive?

You're over a hundred times more likely to be in the second group.