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botany
Apr 27, 2013

by Lowtax

GAINING WEIGHT... posted:

Yes. The second case seems more likely because you have 2 options per die, but you have to subtract out the cases where you get 2 sixes or 2 ones, which is not the outcome you're looking for. Both are 1/36.

answer A: can we please play poker some time.

answer B: https://www.geogebra.org/m/UsoH4eNl

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botany
Apr 27, 2013

by Lowtax
oh god this thread is giving me flashbacks to me teaching an undergrad class about the monty hall problem. jesus that took a while.

botany
Apr 27, 2013

by Lowtax
I mean, at some point you might as well chuck the hotel metaphor and just talk about the underlying mathematics - the natural numbers plus the natural numbers still map one-one onto the naturals, while the reals don't.

botany
Apr 27, 2013

by Lowtax

Phyzzle posted:

The paradox is that anyone is good at maths.

Seriously, that's called Quine's Paradox or something. That manipulating little symbols by human-made rules and syntax can match the behavior of nature so well.

you're thinking of the Miracle of Applied Mathematics, which goes back to the physicist Eugene Wigner.

botany
Apr 27, 2013

by Lowtax

wateroverfire posted:

But I'm not following you here. Each flip is an independent event, right? If someone shows you that one flip was T, the probability that the other flip is H is still 50%. That's what it means for events to be independent of one another.

HH
HT
TH
TT

I show you a T. Viable options left:

HT
TH
TT

in two of those options the other coin is H, in one of them the other coin is T. 67%.

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botany
Apr 27, 2013

by Lowtax
alright honestly this has been explained over and over in the thread, but the example here is so simple that you can actually just do it yourself.

take 2 coins out of your wallet, throw them around the house like 20 times. if they land HH, ignore that throw. then make a list of how often TT comes up vs how often TH (or HT) comes up.

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