There are lots and lots of cases where mathematical models falsify our intuitions. There are also studies that show our intuitions are pretty darn irrational.
Is there a conclusion you want to draw from this? In other words, are you going somewhere with all this?
Here is an example where one's intuition fails, and math shows that it is wrong:
I've never had a problem with that situation, you have a 2/3 chance of being wrong in the first place and should you switch you will always win, thats the first thing i thought when I first heard about it. Maybe if you don't actually think about the situation at all or have no understanding of probability whatsoever you would think that switching gives a 50/50 chance.
I've never had a problem with that situation, you have a 2/3 chance of being wrong in the first place and should you switch you will always win, thats the first thing i thought when I first heard about it. Maybe if you don't actually think about the situation at all or have no understanding of probability whatsoever you would think that switching gives a 50/50 chance.
If that's so, you have above-average logical thinking skills.