So let's get this shit sorted out. If you flip a coin nine

>>36538363
the probability would be 50% just like everytime you flipped it

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>>36538363
Exactly nigger % chance of rain on a Tuesday in July

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>>36538376
But that makes no sense mathematically?

Its 50% each time

>>36538413
past results don't mean shit

>>36538413
how does it not make sense a coin has two sides so you have a 50% chance of it landing on one side

>>36538429
>>36538442
Explain the math then, also the chance is not 0.1 = 10%, but it gets closer to it when n increases, just like the f(n) only gets closer to 0.5 = 50% when n increases

>>36538465
Meaning if you flip a coin n times, it's not guaranteed to have an equal number of heads and tails but it gets gradually closer with each flip

>>36538363
It still 50%, but the probability of flipping a coin ten times and getting tailed ten times is 0,5^10

>>36538465
>Explain the math then

50% probability of H
50% probability of T

Past flips are completely irrelevant. They don't affect the flip in any way.

>>36538489
The probability of getting heads 10 times is 0.5^10
sure, it's possible but not probable

>>36538485
>>36538521
The only two people to get the correct answer in the thread so far.

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>>36538363
what overkill photoshopping that pic.

>>36538699
He worded it in a confusing way

There's a difference between "probability of flipping tails 10 times in a row" and "probability of 10th flip being tails"

>>36538755
>If you flip a coin nine times and it's tails, what's the probability of it being tails the tenth time in the sequence?
>in the sequence?
brainlet much?

>>36538363
Not enough information provided to perform an accurate calculation. Is the coin biased or unbiased? Based on previous information, you'd suspect it's biased towards tails, but you've no real idea of how much so.

>>36538780
>he's too much of a brainlet to do the calculation for a fair coin since the probabilities for an biased coin weren't given
When you try to act superior, you just end up looking dumb.

The question is worded pooely. It's 50/50 because the past flips already occured, but it would be 0.009765625 pwrcent cbance to land on tails ten times in a row. Its just 1/2 chance each time, leading to 1/1p24 chance of getting tails 10 times in a row. However, once tje last flip is ready and the other flips have occured, its rchance is increased to 50%.

>>36538780
The answer is always 50%, because biased coins are impossible to make. Weighted dice only work because they bounce a few times before they settle. When you flip a coin properly you catch it in the air. It doesn't matter how the weight is distributed, it always spends half the flight time in each orientation.

1 time: 50%
2 times in a row: 25%
3 times in a row: 12.5%
4 times in a row: 6.25%
5 times in a row: 3.125%
6 times in a row: 1.5625%
7 times in a row: 0.78125
8 times in a row: 0.390625
9 times in a row: 0.1943125
10 times in a row: 0.09765625

If you've already flipped it 9 times and asking us what the probability is if you're 10th flip is tails, however, it's 50%.

>>36538958
A biased coin is theoretically possible if you add a motor and sensor to actively move the weight about inside it while it's spinning. This would be very difficult to build, especially as it would need to be silent.

>>36539063
Your percentage is wrong. The answer is (1/2)^10. 2^10=1024. 1/1024=0.00097656. Please learn how to do basic algebra.

it would be 50% because the past flips don't affect in any way the final result.

The probability at the start is 0.09765625%
The probability if you reach the 9. coin is 50%

But its already very unlikely that you will reach the 9. coin.

>>36539202
He multiplied it with 100 to show percentage you fucking moron.

>>36538958
>When you flip a coin properly you catch it in the air.
Then glance at it, and either call it good there if you like it, or slap it on something else to change it?
A proper flip falls to rest.

>>36539298
You catch it, then slap it down on the back of your hand so it's obvious you didn't look at it.

>>36539298
>>36539327
Why would you slap a coin retards? Just make your bets before throwing it

>>36539260
There was no percentage sign you moron.

>>36538363
100% both sides are tails

>>36538376
>>36538417
Only for fair coins.

>>36539442
>Balance coin on finger.
>Flick it with your thumb.
>Catch it out of the air in your closed hand.
>Without looking it, slap it down on the back of your other hand.
This is the standard way to flip a coin. It makes it obvious you didn't cheat.

>>36540123
Show me an unfair coin. They don't exist. Coins don't roll and bounce like dice.

>>36538726
We wuz brains

>>36538363
It's 50% every time, however the chance of getting 10 heads or 10 tails in a row is pretty low.

>>36540179
Or you could just
>place your bets or negotiate what you are going to do on heads/tails
>flick coin in air
>let it fall on the table
>????
>done with no stupid bullshit

also coins aren't 50%, they have different markings on each side making them different weights

>>36540271
yeah but you can also split the sequence up in two parts like 5 and 5 throws and as
>>36538413
shows the probability of getting one side depends on the 5 previous throws, as the entire sequence gets closer to 50/50

>>36540290
>>let it fall on the table
>coin slides off the table
>cheater easily turns it over while it's on the floor

>they have different markings on each side making them different weights
It doesn't matter:

http://www.stat.columbia.edu/~gelman/research/published/diceRev2.pdf

WHEN ARE YOU MORONS GOING TO REALIZE THAT EACH COIN FLIP IS A SEPARATE SCENARIO. EACH FLIP HAS NO BEARING ON THE OTHER ONES.

Therefore, the answer is 50%!

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>>36538413
Because it's the WEAK Law of Large Numbers. Yes you get closer the expected value, but we're talking n >= 500. You could get tails 20 times in a row and it wouldn't be uncommon. Whenever probability seems strange to you or illogical consider two things. One, humans don't instinctively get probability or statistice. Two, humans struggle to comprehend randomness.

>>36540350
no you retard, in a sequence the ratio of n coin flips gets closer to 50%, therefore in any point of the sequence you can predict the probability of the next throw.
It works better the more you throw, on 10 coin flips it's nothing visible but try a million coinflips and it's true

>>36540379
No, it applies universally, even in 2 coin flips but the sequence is too small to make accurate predictions out of it.

>>36540420
The size of the sequence has zero influence on your ability to predict any specific coin, *unless* the coin is biased, except biased coins don't exist.

>>36540438
The size of the sequence has influence on how close the ratio of the throws gets and it's subsets, which can be used to predict throws.
God just learn math

>>36540420
What the hell are you saying?
>>36540438
This is essentially true as the odds are always 50%
>>36540461
This is true because of WLLN however prediction is a whole other beast that humans are awful at. Just because you got a hundred tails doesn't mean you can't get a hundred more. You always have a ~50% to be wrong predicting a coin flip.

>>36540461
https://en.wikipedia.org/wiki/Gambler's_fallacy

However, if the coin is biased then making more throws gives you information about how it is biased, which lets you better predict the result. This doesn't matter because biased coins only exist in the imaginations of math teachers. In reality making more throws never helps.

>>36538376
>>36538417
>>36538429
>>36538442
>>36538485
>>36538489
>>36538755
>>36538882
>>36538958
>>36539063
>>36539223
>>36540271
>>36540502

I am glad there are so many big-brain anons in this thread. The other one was full of literal retards

>>36540506
You are enlightened.

If you answered something other than 50% and didn't get a (You), you are officially a brainlet.

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>>36540630
I love problems like this anon. Too bad my math degree didn't get me a job. I guess that's one problem math can't prove.

>>36540502
>>36540506
Morons, as I said you can predict the number of heads in a sequence if you analyze the sequence in multiple parts. It does give you the power to predict an individual coin flip in the sequence too, if you know what average the sequence is getting closer to, but the added chance is just so small it doesn't matter in real life. However, the small chance is still a chance.

>>36540743
And remember brainlets, I'm not talking about an individual (1) coin flip, I'm talking about an individual coinflip in a larger sequence.

>>36540743
>analyzing a sequence of random events gives you a chance at predicting the next random event

You are incorrect, unless you are talking about computer-generated pseudorandom numbers.

>>36540777
Wtf are you smoking man?
Analyzing sequences is based on the fact that the probability of one heads is larger than 10 heads in a row.
That is exactly what's going on here, I gave you the mathematical proof but you still go on about your 50% in a single coin flip, where it's the whole sequence and it's subsequences we are interested in.

Jesus.

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>>36540743
There is no added chance. That's what we've been saying. As >>36540777 said, this isn't some computer based reality where prng is enforced. We are living in our current universe of true randomness. You could "analyze" (nice meme word) a sample of 500 straight tails and you'd still only have a 50% chance to be correct. This is why Vegas works. People like you think they will eventually see the desired odds and millions are thrown away because
>lmao stats is hard

>>36540869
>People like you think they will eventually see the desired odds and millions are thrown away because
I wouldn't throw my money away for a chance like that, since in a million coin flips the added chance added is 0.5^1000000, which is hardly nothing, but just because it's small doesn't mean it's nothing. Just read a book dammit.

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>>36540931
My friend, there is no added chance.

Here is a proof of why the answer is 1/1024.
The question asks for the probability of the tenth toss being tails GIVEN the previous 9 tosses were also tails. Because getting heads or tails from a coin toss are independent events, P(AnB)=P(A)*P(B). Define event A_n as the nth toss being tails. Clearly, the P(A_n)=1/2. We are looking for P(A_1nA_2n...nA_10), in other words the probability that the first toss was tails and the second toss was tails and...and the 10th toss was tails. Using the identity stated above we obtain that our probability is P(A_1)*P(A_2)*...*P(A_10)=(1/2)^10=1/1024.

All you other faggots are wrong.

Which way is the coin facing before it's flipped? Because coin flips aren't 50/50.

>>36541057
Mathematically, there is. You can't get a heads 140% of the time can you?
Therefore if the set get's closer to 50% and the previous set was 90%, the next set must get closer to 10% for the whole set to get closer to 50%
It's not set in stone though and the more you throw the coin the more you can predict the sets but the harder predicting an individual coinflip in the set becomes. This is not hard man.

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>>36541121
If the chance changed after each trial not only would you not have IID but you would also be, theoretically, always approaching a moving target. The chance is 50% at n=1 and 50% at n=1000. The only "chance" that increases is that you get closd to your expected value. The actual chance of the coin flip is unchanged.

>>36541187
The target changing every flip doesn't mean it's wrong though.

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>>36541340
Well then you don't have an IID rv so all of your theory is thrown out the window. Have fun inventing a new field of stats based around the nonlinear.

>>36538413
That shows you the probability of the coin getting tails 10 times in a row BEFORE you flipped the coin. Every individual coin has a 50/50 chance

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>>36538485
>>36538521
This. Anons just need to realize the probability of a particular sequence of results is separate from the coin flip itself. Yes, it is obviously less probable to get 10 tails in a row. But regardless, on that 10th flip the probability of it being tails is still 50% regardless of the previous outcome. That's why for example correctly predicting 3 heads in a row, then thinking "I got 3 heads in a row, there's no way I'm gonna hit heads again" and predicting tails is completely wrong. It will always be 50%.

You idiots are too blinded by too much learning probability and thinking you can apply your "logical thinking" to this.
No, the coin will NOT still be 50/50 after consecutive same side of the coin.
The coin gets loaded by imbalance in the universe so the energies will even out with time, therefor it's not 50/50 anymore.

Try refute it best you want, but if you flip it 5 million times it will be close to 50/50 results, so if you get the same many times in a row, it will get less then 50/50 due to the evening out effect.

People like you are always so easy to con. And you're bad at the stock market.

>>36538363
>Wattamellum

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>>36542231
>imbalance in the universe so the energies will even out with time
hmm

>>36542282
The universe is a "zero sum game". If you add upp everything that exists in the universe it evens out.
All the positive charge from matter is cancelled out by the negative charge of gravity and so on.
There's 0 energy when you add it all up.

Same goes for probability. That's why the coin is 50/50 but it can't be 50/50 at each flip, only in theory. But not in practical reality, which is the only thing that matters.

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>>36542521
I'm sorry anon but this is some bullshit. I hope by the even forces of the universe this is bait

>>36542719
No, it's not bullshit.
Why is it? Explain.
Only reason you think it is is because you don't understand the universe is a process rather than platonic.
And as I said, energies are completely even in the universe, it's the only reason it can continue existing. This will affect probability as well.

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>>36542783
Lay off the vsauce nigga

>>36542814
>vsauce
Had to goole this and have never seen.
You mean lay off my superior thinking and reading of physics and philosophy.
But no.

You don't have to listen but this is reality. I fyou know it you'll be better able to seize opportunities.

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>ITT: brainlets so far gone they don't even understand how coin flipping probability works