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.

Well then how does switching your chosen door help you increase chances 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

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A great account of the lesson, but you need to ensure that you go beyond a mere description of what went on in the lesson. Please try to reflect on the key knowledge issues as that it is the only way you will be able to consolidate and develop your TOK thinking.

This is excellent work again Tamaki. But you need to remember why it is relevant to TOK. That is because it is a good example of how the intuition can give you one solution whilst reason gives another. It also shows how much people will support their initial ‘gut’ feeling without testing their claim in a more rational manner.