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Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 149

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alexeymosc: Wrote a detailed reply in a private message.
The probability of winning is very high compared to what it seems at first.
Mathemat:
The probability of winning is very high compared to what it seems at first.
They have exactly the same strategy and the challenge is just to find the optimum probability of sending a response. Am I right?
Mega-brains don't communicate. Is it possible to say that they can choose their probability of sending a message under the terms of the problem? That would mean that they got together and decided "we will send a message with a probability of 0.75".
alexeymosc:
This would already mean that they got together and decided "we'll send the message with a 0.75 probability".
No, it would mean that they understood and found the optimality.
TheXpert:
No, it would mean that they have understood and found the optimality.

I see, then my answer is: send a letter with a probability of 0.1. If MM came to this conclusion, the probability of getting a win is 0.5.


There is a clear rationale )

alexeymosc:

I see, then my answer is: send a letter with a probability of 0.1. If MM has come to this conclusion, the probability of winning is 0.5.


There is a clear rationale )

0.5 won't work. There's 0.39 roughly (0.3874). Something you did wrong with the formula.

C(10,1)*x*(1-x)^9.

Hmm, I didn't really get it all myself. Now it's clear how your answer works out.
(4) For Mega Brain Day, N name T-shirts were issued, strictly one per person. The megabrains were supposed to enter the room one by one in a certain order, find their T-shirt, put it on and leave. But unfortunately, the first megabrain dropped out of action and was replaced by a mini-brain, who didn't have time to get his own T-shirt. The procedure remains the same, but the mini-brain enters the room first and puts on any T-shirt it finds. Next, each megabrain, if it does not find its own T-shirt, puts on any other of the remaining ones. What is the probability that the last person to enter the room puts on his T-shirt?

Is the proof (conclusion) needed? Because that's exactly the point, if I've counted it correctly.

TheXpert:

Do you need a proof (conclusion)? Because that's exactly the point, if I've counted it correctly.

Conclusion - in a private message, if you want. Or a brief substantiation.

Otherwise a numerical answer will suffice. My answer is surprisingly simple. I don't know if it's right or wrong yet.

I'd love to see the conclusion if it's simpler than mine. I have five lines of formulas and the same number of explanations.

1...142143144145146147148149150151152153154155156...229
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