[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 394
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I'll try again.
Putting ourselves in the presenter's shoes.
We know where the prize is, as we put it there ourselves. Let us also know that the player has chosen a strategy and will always change his choice. Should we play with him?
The player with equal probability of 1/3 can point to each of the three boxes. And if he chooses the box where the prize is (we know about it!), he obviously loses, because he will change his choice anyway. The probability of this outcome is 1/3. If the player will choose any other box (1/3+1/3 - both are empty!!!), we as a leader will be forced to open the second empty box (we won't open the prize right away!!!). But then the player, by changing his choice, gets the prize.
That's it, I don't know how to elaborate any more.
I'll try again.
Put yourself in the presenter's shoes.
We know where the prize is, as we put it there ourselves. Let us also know that the player has chosen a strategy and will always change his choice. Should we play with him?
The player with equal probability of 1/3 can point to each of the three boxes. And if he chooses the box where the prize is (we know about it!), he obviously loses, because he will change his choice anyway. The probability of this outcome is 1/3. If the player will choose any other box (1/3+1/3 - both are empty!!!), we as a leader will be forced to open the second empty box (we won't open the prize right away!!!). But then the player, by changing his choice, gets the prize.
That's it, I don't know how to elaborate any more.
Mishek wrote correctly out of 100 cases there will be a 98% probability, but in reality?
Guessing boxes or 2 that are 50/50 or closed 3 that are 33% - that's it! nothing else is involved in the experiment, and is a distraction - let him stand on his head, the audience is polling....
And the real show has three doors, not two - because people are intuitive and will more often guess....(except for mathematicians).
I admit it's 50/50 wrong, I'm confused about this, I'll save it for later
For me, a simple way to get the right answer is to reason: In two cases out of three, I choose an empty box and the presenter opens the second empty box. In two cases out of three.
Recall Field of Wonders - two boxes right - left - right - left - left - right - 5 choices out of two. You can add one open box to the side. Good luck!
Why don't you try to count with someone in person? Do at least thirty experiments, it won't take long, honestly. You will see for yourself. Otherwise, you are like an unbeliever - no, and that's it! People have been checking for twenty years before you, and the mathematical solution to this problem has long been known. Why should you bend your horn? I do not understand it.
A simple arithmetical problem.
One mathematician visits another for a beer.
-Hello!
-Hello!
-How's life?
-Fine, I'm doing theorems, my wife's around, my kids are growing up.
-Oh, you have kids, how many are there?
-Three.
-How old are they?
-You know, the sum of their full years equals the number of windows in that house across the street.
-That's not enough information for me to know the age of your children," he said after counting the windows in the house across the street.
-And the product of their full years equals your age.
-He, still not enough info.
-Well, what else can I add? Except that my youngest is a redhead.
-Oh,then your kids....
How old are the kids?