A brain teasing probability puzzle

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khalid

khalid

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a_skeleton_03_sl said:
Yeah, we use it for important things like whether we will get a goat or a car on a game show.
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This is an artificial example sure, and if you go back to see my original posts on this thread, I mentioned that this thing is really brought up mainly to "gotcha" people who haven't heard the puzzle before.

However, it does clearly showcase that human "intuition" is horrible at conditional probabilities. That is why we need to use probability more and not let so many things be ruled by intuition.
 
ZyyzYzzy

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All this unintuitive logic probably stems from the fact that humans are initially wired to think logrithmically.
 
Tuco

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The Ancient_sl said:
You think the difference between 1:2 and 1:4 is equivalent to 1:512 vs 1:1024? Seriously?
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In that 4/2 = 1024/512, yes.

I don't know what you're arguing or are asking.

and lol @ a_skeleton_03 saying we rely on probabilities too much because the math is too hard. I really miss intrade =\
 
Tuco

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Ancient come at me bro.

The chances of getting N heads in a row are always twice as likely as getting N+1 heads in a row. That's all I'm saying. Doesn't matter if N = 1 or N=9.
 
N

Northerner

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Ugh, that certainly was *not* my point a_skeleton_03, although you are welcome to your own conclusions of course.

We suck at intuitively interpreting statistics because our brains are wired to seek patterns even where none exist. It has been a successful strategy. The answer to this is to learn the mathematics and get real working results even though our brain tries to trick us.

You can argue whatever you want but statistics works.
 
T

The Ancient_sl

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Tuco_sl said:
Ancient come at me bro.
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SUP BRO
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T

The Master

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a_skeleton_03_sl said:
Which is why I hate that we rely on probability the way we do and how we attach science to it so much.

There are too many variables in a decision to really make math all that relevant.

See earlier my comment on a coin flip. There are soooo many things that can affect the outcome of simply throwing a small round and flat piece of metal into the air. The warmth of your hand effects it and ruins everything.

Each event should take place in a vaccuum. A coin flip is 50/50 no matter what came before or what will come after it.
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The use of statistics in science was discovered a couple of hundred years before computers and was therefore a "useless curiosity." We knew it would work but doing the computations by hand was untenable. Come the Manhattan Project, John von Neuman and Stanislaw Ulam realized computers had reached a point where they could be used to run statistical models. Most people being bad at probability intuitively and being to ignorant to understand it is not an argument for not using it, it is an argument for education.

You realize this math applies to any random binary decision, yes? Also if there were an outside variable influencing the results we would know about itbecauseiterative tests weren't matching the expected probabilities by a certain margin. We would know that margin because of statistics. So we'd need to go find the variable. You'd be stunned at how much science is discovered by "Oh, it should be working this way, but it isn't, what are we missing?" That is a benefit of testing statistical models against reality, not a con.

Each coin flip is 50/50. The total potential combinations of N coin clips where N is greater than 1 is not 50/50.
 
iannis

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It reminds me of that picture where they imaged a molecule this past year. I'd always thought the way you diagram in chemistry were just simple representations of how shit works. I'd basically preassumed that while the shapes of proteins are obviously their most important and obvious facet, they're magnitudes of scale larger than simple molecues and there comes a point where our spatial understanding is just no longer relevant. Without even thinking about it I'd decided that those diagrams are mathematical abstractions which adequately represent the truth in a pliable form but are not themselves the truth.

Then I saw that picture and was like, "Well... motherfuck. Would you look at that?" As you get older those pure "woah" moments get spaced further apart. But that was a woah moment. Hundreds of years ago men correctly intuited the basic structure of matter using not much more than obtuse observation and parsimony. I think math is worth a shot.
 
Tuco

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Iannis you talking about

triptych350.png


?

I'm surprised you're surprised it looks like that.... I always thought that molecular diagrams were somewhat accurate (If arbitrarily 2 dimensional) representations of matter.
 
hodj

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Iannis_sl said:
It reminds me of that picture where they imaged a molecule this past year. I'd always thought the way you diagram in chemistry were just simple representations of how shit works. I'd basically preassumed that while the shapes of proteins are obviously their most important and obvious facet, they're magnitudes of scale larger than simple molecues and there comes a point where our spatial understanding is just no longer relevant. Without even thinking about it I'd decided that those diagrams are mathematical abstractions which adequately represent the truth in a pliable form but are not themselves the truth.

Then I saw that picture and was like, "Well... motherfuck. Would you look at that?" As you get older those pure "woah" moments get spaced further apart. But that was a woah moment. Hundreds of years ago men correctly intuited the basic structure of matter using not much more than obtuse observation and parsimony. I think math is worth a shot.
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You're actually still right. The molecular diagrams are accurate, but there are lots of simplifications and handy rules of thumb that don't actually model reality exactly but do so close enough for fast and dirty work. Resonance and hybridization aren't exactly accurate representations of reality, but as ways to help people visualize the concepts and as a fast and loose method they work really well so they hang around even though some people wish they didn't.
 
BrutulTM

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Northerner_sl said:
The fun bit is that the odds of getting the sequences of H-H-H-H-H-H-H-H-H-H and H-T-T-H-H-H-T-H-T-T (or any other sequence of events) are identical. Our brains suck at probability.
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Yeah and 1, 2, 3, 4, 5, 6 is just as likely to come up in powerball as any other numbers you could play but I bet nobody plays those because that seems impossible to get.
 
Hachima

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BrutulTM_sl said:
Yeah and 1, 2, 3, 4, 5, 6 is just as likely to come up in powerball as any other numbers you could play but I bet nobody plays those because that seems impossible to get.
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But I'm sure there are some that do.Then if you win there is a higher chance you have to share the winnings.. screw that.
 
N

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BrutulTM_sl said:
Yeah and 1, 2, 3, 4, 5, 6 is just as likely to come up in powerball as any other numbers you could play but I bet nobody plays those because that seems impossible to get.
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Actually, decades ago I used to play 1 through 6 whenever I bought a lottery ticket for exactly that reason. Then I thought about it a bit and realized that there would be others doing the same thing and on a win I would be splitting it too many ways.

Thenl I just decided that lotteries were stupid anyhow.
 
BrutulTM

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Anyone who can understand probability well enough to do that can also understand it well enough to not play the lottery.
 
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