Counter Intuitive Maths – The Monty Hall Problem

I found the concept of counter intuitive maths very interesting as it applies to many situations I have faced, like sitting a multiple choice test. Counterintuitive is something that goes against what you believe to be right based on common sense or logic. Learning about the psychology and thinking process behind it has been interesting as I have found myself thinking the same when carrying out a quiz or making a decision. An example of counter intuitive maths would be taking a multiple choice test. You decide that the answer is A but then you have a moment of doubt and second guess your answer, as you think it might be B. The majority of people won’t change their answer. This is because if you change your answer and then get it incorrect it has more of a negative impact on you than if you stick with your answer and get it incorrect. There is too much of a risk and so people stick with the safe option. I am in the same boat and tend not to change my answer if I doubt myself, however, is this the mathematically correct thing to do?

We looked at The Monty Hall Problem to test this and the results are pretty fascinating. If I think about this too much my brain hurts, but when I look at the basic principle of the concept I understand the Monty hall problem. I am applying my knowledge of fundamental maths to understand this.

Pretend you are on a game show, there are three doors, behind once is a brand new car, behind the other two are goats. You pick a door, and then the host opens one door revealing a goat. He then gives you the chance to change to the other door. If you stick with your original door there is a 1/3 chance you will pick the car, however, if you change to the other door, you are giving yourself a 2/3 chance of winning the car. This picture explains It more clearly.

You are not guaranteed to win the car by changing your answer however you are increasing your chances from around 33% to around 66%. Therefore, you have a better chance of winning the car by changing your answer. This has made me re-evaluate my thought process and I will now be making sure I go with my second answer to increase my chances of success.

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