A brain teasing probability puzzle

Tuco

Tuco

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Hoss_sl said:
No, I'm saying that if the theoretical results don't pan out in the real world, then the whizzards of smart must have missed something. They are human, after all. Any theory that can't pass a practical test is a bad theory. You'd have to be a simpleton to trust what's written out on paper over actual results.
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Where did you get your degree?
 
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The Ancient_sl

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A coin has a 50/50 chance of being heads or tails on a given flip.

If I flip a coin 10 times what are my chances of getting all heads?

Now, I've flipped a coin 9 times and gotten all heads. What are my chances of getting heads on the 10th flip?
 
ZyyzYzzy

ZyyzYzzy

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It is unlikely that if you flip a coin 5 times you get heads 5 times in a row.

It is unlikely that if you flip a coin 100 times you won't get heads at least 5 times in a row.

Math, more mysterious than magnets.
 
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The Master

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a_skeleton_03_sl said:
No, still 50/50. The other 9 flips have no bearing on the 10th flip.

EDIT: Are we allowed to say "flip" on the forums?
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No, the odds of getting heads 10x in a row is .5^10. The odds of any given flip are 50/50. Not quite the same thing.

You can work this out with the simpler scenario of 2 flips, which gives you three potential combinations. Heads/Heads, Tails/Tails, and Heads/Tailsx2. So the odds of each of those scenarios is 25%. Heads/Tails has two combinations, so that is 50%. What is .5^2? .25. Make sense?
 
A

a_skeleton_03

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ZyyzYzzy_sl said:
It is unlikely that if you flip a coin 5 times you get heads 5 times in a row.

It is unlikely that if you flip a coin 100 times you won't get heads at least 5 times in a row.

Math, more mysterious than magnets.
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You mean the human mind is mysterious.

Every flip of a coin is only 50/50 ever. We assign all kinds of importance to multiple which do nothing to explain the actual probability but expose the flaws effecting the flip.

You flip it 100 times and it comes out heads every time you have two options on why.

1.) Total RNG
2.) Environmental variables. e.g. Wind, humidity, hand dexterity, unbalanced coin, what have you....

A coin is always 50/50.
 
BrutulTM

BrutulTM

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I did that simulation 4 times and switched every time and I got the car all 4 times. Then I did it once without switching and also got the car. Clearly either option yields 100% success so this whole thread was pointless.
 
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The Ancient_sl

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What are the odds of getting heads on 9 flips vs getting heads on 10 flips? How can there be such a large disparity between these 2 numbers if your last flip is truly 50/50?
 
Tuco

Tuco

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Its .5^9 vs .5^10
Its not a huge disparity, one is twice the likelihood of the other.
 
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Northerner

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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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a_skeleton_03

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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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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.
 
iannis

iannis

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Reminds me of a picture of a quarter standing up on edge captioned with, "Fuck you and fuck your math"
 
khalid

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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.
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Uggh, if anything we as a society should rely more on probability and science. The problem is the general lack of knowledge on the subject and not how often it is used.
 
A

a_skeleton_03

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khalid_sl said:
Uggh, if anything we as a society should rely more on probability and science. The problem is the general lack of knowledge on the subject and not how often it is used.
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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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