[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 602

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vah:
They throw 2011 times the numbers equally, then they throw 2012 times, then there is a 50/50 chance


but if it's not 2011 and 2012.

1000 и 2000 ?

 
vah: They throw 2011 times the numbers equally, then throws 2012 times, there is a 50/50 chance

Nizachod. All possibilities are considered in the terver.

Mischek2: how about not 2011 and 2012 but

1000 и 2000 ?

No. The parameters of the problem are chosen specifically. If the difference is not equal to 1, then the elegant solution does not work.

 
Mathemat:


No. The parameters of the problem are specifically chosen. If the difference is not equal to 1, then the elegant solution does not work.


I wrote to vah

))

 
Mischek2: I wrote to vah.
Well, I wrote you back as well.
 
Uh, 3/8? ... wrong
 

I can see that there aren't many people willing to do that. OK, one more (3 points):

Megamozg bought a 53-pack of apple moth repellent. The product starts working three days after it is applied to the tree. However, he discovers that one of the packs is defective and also repels the fruit pollinator, without which no apples will grow. Megamogg can't risk his orchard, but he has six wild apple trees on which he can test the repellents. But after six days, the apple moth starts to go on a feeding frenzy, and there won't be much left of his orchard if he doesn't treat it. How can Mega Brain find the defective product and save his crop?

Note: we only have 3 days in which to identify the one defective pack. In fact, we have only one treatment attempt - on Day 0. Earlier than Day 3 we have no way of knowing anything.

If we are late and pollinate the trees with the "right" repellent later than 3 days, the fruit moth will devour everything instantly on Day 6 and will not wait for the repellent to work (it also starts to work after 3 days).

P.S. Those who know the solution approach, please do not write an answer here. Not knowing write only in private.

vah: ммм 3/8? ... ошибся

The correct answer - exactly 0.5. Justification will not lay out here, suffer.

 
So there are eight outcomes, 4 of which we are satisfied with, right?
 
Why eight? There are a hell of a lot of outcomes - I don't even know how many really are.
 
Mathemat:
Why eight? There are a hell of a lot of outcomes - I don't even know how many really are.
it's at the end of eight again I must have thought wrong again, 2010 to take as I thought the probabilities of both are the same, that leaves three throws i.e. eight outcomes 4 of which satisfy us =(
 
vah: As I thought the probabilities of both are the same, there are three throws remaining, i.e. eight outcomes 4 of which satisfy us =(
Neither the last 2012 throw, nor the last 3 throws have a significant effect on the probability of the second player having more odd outcomes. It's not obvious, but it does ).
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