# A Fantastic Introduction to the Concept of Bayesian Statistics

## All you need to know to solve this Cambridge University entrance problem is Bayes’ Theorem

I recently came across this very hard looking and creatively articulated problem in an old entrance examination paper for Cambridge University. When I first looked at it, it seemed very complex. But one thing I have learned from years of practising Math, is that if you don’t immediately know what you are doing, take the time to write down the information you have. Often in the course of doing so, a method will reveal itself.

Let’s start with the question. Here it is. It gave me a little giggle to think about how writing a question like this is probably one of the rare opportunities the writer had to try to be creative 😂

## Writing down the information

There is a lot of information given here, so I decided to write it all down in some useful format before even tackling the question asked. Since the question primarily deals with combinations of ties and trousers, I decided a simple table would suffice to capture the information, so I created a table with the trouser choices in the rows, and the tie choices in the columns. Each cell in the table is the probability of the tie choice given the trouser…