[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 392

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Vita:
Even without cheating, an experienced accountant's eye, for example in paragraphs 29-30 29-30 immediately says "I don't believe", or in item 35 we see that 4*7 = 22, which again indicates a false. Altogether counting only two-digit examples and estimating probability of the rest you get 35 points at once.


Monty Hall's paradox
There are three boxes: "A", "B" and "C", one of them contains a prize, the others are empty. You choose "A". The presenter knows exactly where the prize is and first opens the obviously wrong choice "B", showing that it is empty. Then he asks if you want to change your choice. Now you have the option to stay with option "A" or change it to "C".

Is it worth changing your choice and why?

It's considered worthwhile, but I think it's nonsense.
 
Mischek:

It's considered worthwhile, but I think it's nonsense
Delusional - intuitive or reasoning?
 
Vita:
Delusion - intuitive or reasoning?
intuitively
 
Mischek:
intuitively
That's right, the task is specifically designed to challenge intuition.
 
looked at the evidence. That's bullshit, that's cheating.
 

If we don't change our choices, it turns out that we initially guess only one box out of three, because the presenter opens his box after we have chosen it.

If we always change our choice, it's equivalent to choosing one box that won't open, but the other two will definitely open - hence the statistical advantage - we win in two out of three cases.

 
The cornerstone of the proof is that the strategy is pre-determined: either always change, or always stay with your choice. If, on the other hand, you act from scratch every time, for example by flipping a coin, the probability of winning is exactly 50%.
 

>
 
alsu:

If we don't change our choices, it turns out that we initially guess only one box out of three, because the presenter opens his box after we have chosen it.

If we always change our choice, it's equivalent to choosing one box that won't open, but the other two will definitely open - hence the statistical advantage - we win in two cases out of three.

Two will still be open 1,2 or 2,3 - the first will be open to check the presence of the prize. (If you have a strong intuition, the first choice will be the right one)
 
Tantrik:
Two will still be opened 1,2 or 2,3 - the first will be opened to check if there is a prize.

no. Choosing one box that you definitely can't open is like choosing two boxes that you can open.

And if you choose one box to open (we can only open one ourselves), then the master will still open the empty one.

logic.

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