# Maths, Stats and Think Traps – Confirmation Bias

Hello there! This is the 1st of a 3 part post about some of my favourite (and most common) issues in data science. I have learned about them a while ago in college and books but since the start of my career I have also seen them in the wild. I first saw this one on a book called ‘Tricks of the Mind’ by Derren Brown. In a nutshell, it goes like this:

Let’s assume you have these 4 cards:

All you know about them is that each card has a letter on one side and a number on the other. Now, at some point someone tells you that

Every card with an A on one side will have the number 3 on the other

Which cards do you need to flip to prove that this statement is correct? Give it a proper go.

Most people would answer A or A and 3 but actually neither of those answers is correct. Let's review the cards one by one:
• Card A - You obviously need to flip this one. If there is any other number than 3 behind it the statement becomes false.
• Card D - If there is a 3 or any other number nothing changes. We said A implies 3, not 3 implies A.
• Card 3 - For that very same reason, if you had an A behind it then that would be fine. If you didn't, that would also be fine. We don't really need to flip this one.
• Card 7 - At this point you might have already gone 'ah!' and realized that if the card had an A on the other side then the statement is false.

This is obviously an oversimplified example of the problem but I have seen this sort of thing happen in so many different situations that I though I should write a post about it. Anyway, this is me for now, let me know what you answered and see you on part 2 – Bayesian Traps, goodbye!