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RE: Paradox is fun! #2 - Will you switch the door? 趣味悖論 #2 - 你會換另一道門嗎?
Here comes the monty hall problem! This one is a must-known for all statistics major students and the situation is just very counter intuitive which makes it interesting. The great lesson we can learn from the problem is that our intuitions could lead to fallacy if we do not build a good foundation in mathematics and this means a great loss, especially when we're always surrounded by numbers!
Yes this problem is really an interesting paradox in applied statistics. Many classes of elementary statistics will touch this simple yet confusing problem . If someone is learning Bayes' Theorems or related concepts abt conditional probabilities, this example will be a good illustration.
True. Back then when I was a student conditional probabilities and distributions were the first few topics to learn and in studying the topic actually there were lot more other confusing problems than the monty hall. Remind me of those days long ago!!
Seem like you are also a statistics major! To me, some statistical concepts are quite counter-intuitive but share really cool ideas. Like when we want to compare the number of points in [0, 1] and [0, 1] x [0,1], the latter is similar "larger" in some intuitive sense but they contain the same infinitely many points. So this partly leads to studies of measure theory which defines sizes in strictly math sense.
yes i'm a statistics major. But I didn't really touch the measure theory.. that sounds interesting. Do you have more to share about it as an introduction? Maybe you would want to write the next post on it, giving some examples and applications. That'd be great!
yes I have come across this problem in my University study as well. it's really a confusing problem when I first read it! but it's really interesting. I think probability is really one of the most interesting topic in maths.