# Lesson 4: Friday 13th September

In today’s lesson we focused on the Monty Hall Problem.

Well here is a simple image that will help you understand what the Monty Hall Problem is:

To summarize this image:

It is saying that the probability of you getting a car (which is something your desire) instead of a goat (which is something you don’t desire) is higher when you switch your chosen door after the first door is opened/revealed.

The door that will always be opened at first will be of one of the goat doors, therefore some people may believe that the probability of getting a car after the door is opened will be a 50% chance because only two doors are remaining and the car can only be in one and therefore switching your choice will not make a difference (because its a 50% chance). However, during the lesson we’ve come to learn that this is wrong.

Well, why is this wrong? Because, as shown on the image^ it isn’t a 50% chance, but instead it is a 2/3rds of a chance of getting a car.

This is because, the first goat door will always be shown, therefore instantly this eliminates a 1/3 (3/3 – 1/3 = 2/3), leaving you with a 2/3 chance of getting a car.

Switching doors is bad only if you initially chose the car, which happens only 1/3rd of the time. Switching doors is good if you initially chose a goat, which happens 2/3rds of the time. Thus, the probability of winning by switching is 2/3rds, or double the odds of not switching.

“Switching turns a loss into a win and a win into a loss,” says Jason Rosenhouse (mathematics professor at the James Madison University), “and since my first choice is wrong 2/3rds of the time, I will win that often by switching.”

How did this affect me, what i learnt from this experiment? and what impact does this have on my opinions on ToK ???

^^ work on this + also try this experiment on mum and review

Useful links: Scientific American – Monty Hall Problem