Thread 16836405

According to gay.i. the chances of a coin landing on heads 100 times in a row is as follows:
>The probability of flipping a coin and landing on heads 100 times in a row is extremely low, calculated as (1/2)^100, which is approximately 0.79 x 10^(-30).

How is this possible when the chances of landing on heads is about 50/50 on any given flip, including the 100th flip.

Please forgive any retardation in my post i did not pass high school, somebody please teach me.

What problem do you see in this calculation? Do you expect this probability to be different? What number do you expect?

>>16836412
im saying the 100th flip is simultaneously 50/50 AND
> (1/2)^100, which is approximately 0.79 x 10^(-30).
how is this possible

>>16836405 (OP)
No one knows, OP. Perhaps it will be you that "cracks the code". Good luck, young analyst. Report back often and frequently.

>>16836417
Is this the reddit board?
If you can't answer just admit it.
Let the smart anons take care of it.

>>16836414
(1/2)^100 is the probability of all 100 flips in a row to land heads. 1/2 is the probability of the last flip to land on heads. Two different events have different probabilities.

>>16836414
It's a problem of observation. To determine whether the coin is an H or a T we need to bounce a photon off it. Photons do not experience time and so already knows the answer before we even pose the question.
Wave function of 100 flips collapses into the final 100th 50/50 toss.

>>16836420
>i don't want the prize
More for me. Sucker.

But seriously ChatGPT is very good and answering such questions in nauseating detail. It will keep explaining it for hours and won't get irritated, tired, ironic. It has infinite patience.

>>16836425
AI is implicitly biased towards irony because it is trained by humans. You're simply to autistic to detect its tone.

>>16836405 (OP)
Because 99 heads then 1 tail is the same chance as 99 heads then 1 head. Both are
>1/2^100
So if it's the chance, that's 50/50

>>16836405 (OP)
Holler if it's not clearly clear.

>>16836405 (OP)
Look at a smaller sample and this should be clear. Let's say 2 flips. All of these are equally likely:
>HH
>HT
>TH
>TT
So the probability of getting two heads in a row is 1/4.

Now let's say these were actually your 99th and 100th flip respectively. We can model possibilities for your 98th flip onwards by making one copy of the list all starting with an extra heads:
>HHH
>HHT
>HTH
>HTT
And then make another copy all starting with tails:
>THH
>THT
>TTH
>TTT
Now there's 8 possibilities. The number of possible outcomes doubled so the probability of seeing any particular one is halved.
Repeat this process indefinitely and the number of possible outcomes is 2^n where n is your number of flips. The probability of getting any one of them is going to be 1 divided by that number.

>>16836405 (OP)
This is a old mathematician's wife tale.
Notice that everyone always focuses on the veracity of the claim that, "you flipped a coin 100 times" and not, "you truly have a perfectly fair coin".
Of course OP has flipped his coin 100 times. I image at this point OP has tossed his pog googillions of times and likely can do 100 in under a minute.
I just don't believe the coin is fair. And no amount of data, in OP's notebooks, journals, white board, walls, mirrors, cat, hdds, ssds, cloud accounts will ever convince me otherwise.

>>16836599
In this scenario, the coin is fair -_-

don't worry, its normal for probability to be unintuitive, we are not designed to reason about probability like we are with your standard numbers, as it is both extremely abstract and also tends to deal with extreme numbers big and small.

the most intuitive way to imagine it is spatially. suppose you are in a room with two doors: one door leads to a red room, the other blue. now imagine each colored room again contains two doors, also each one being either red or blue.

its easy to visualize the probability at your first pair of doors, it is 50-50. you pick a door, go through it, and now it's the same question. each room, you have a 50-50 chance of picking a door and having it be red or blue. consider what would have to happen to walk through three blue rooms: you pick one door, it happens to be blue; pick another, happens to be blue; pick another, happens to be blue. going through a specific series of doors requires a lot more luck. imagine repeating this 100 times and only ever seeing blue rooms.

>>16836405 (OP)
thats how many outcomes there are with 100 heads divided by the total number of outcomes 100 coin flips could have.

real systems are fully deterministic which make probabilities almost useless

>>16836405 (OP)
probability is just determined by summing up all the variables, they don't inherently mean anything.
like, you can take a coin, flip it, it lands on heads, now flip it the exact same way 100 times, congratulations, the probability of your coin landing on heads is now 100%

>>16837316
Prove it.

>>16837331
You are making so many inplicit assumptions about all the doors you will never view. Pretty sure I could jam those doors stuck with 100 or so coins too.

The misunderstanding of this concept is way more common than you think. It's the reason retard people loose their life savings in a matter of hours.
Google gamblers fallacy for an easy explanation.

>>16837485
Don't need to; how about you go fuck yourself instead, you retarded queer.

>>16836405 (OP)
imagine you do just two coin flips, that gives you four possibilities:
both coins heads
1st coin heads 2nd coin tails
1st coin tails 2nd coin heads
both coins tails

there's nothing that makes one outcome more likely than another (and that is precisely because every flip is 50/50, and doesn't depend on what you got before!), so you have 1 in 4 possibilities to get both heads. Now you just add more coin flips and follow the same logic, and for 100 flips you get that very low number.

>>16837851
You simply tell yourself that because ypu can't. But we all know you are a failure.

>>16837862
Wrong again, we all know you're a loser with no friends.

>>16837844
I was one of those millipns of people who lost my life savings, home, and family playing Google's Coin Toss 100 when it was original released.
Coin: Not even once.

>>16837864
Still can't do it, can you?

>>16837868
All night, loser.

>>16837870
Fucking kek. At least you know your limits.

>>16837874
I know you're a retarded queer who doesn't know how math problems work. That's enough.

>>16837883
And you know that for the rest of the night you won't be able to prove that your coin is fair. You are honestly honest. I beleive you when you say that.
>That's enough
You exceeded everyone's expectations today, anon. Good pig.

>>16837888
Don't need to, loser. Keep proving you're too dumb to understand how math problems work.

>>16837895
It's a simple problem in introductory statistics. No calculus required.
Can you do it?

>>16837485
it's axiomatic you dumb fuck

>>16837981
>coins are bits, 0 or 1
Have you never seen a coin, child?

>>16837966
Fuck you, retard. If you want to talk about a different problem, start your own thread or admit politely that you'd like to go off on an unrelated tangent. If you act like an obnoxious retard, all you deserve is vitriol and piss in your face. Asshole.

>>16837997
>50/50, like every dice, kys btw
>i assumed it
>mic drop
Their level of ignorance is surpassed only by their level of anger.

>>16837999
>I can't read
Fuck you, retard.

>>16837997
>you derailed a slide thread
>reeeeeeee!
Pathetic. Utterly pathetic.

>>16838006
>Please forgive any retardation in my post i did not pass high school, somebody please teach me.
No. You are a sad, ugly person.

>>16838007
>>16838011
>I can't read and/or got mad when a smarter anon called me out on my bullshit and my bad attitude.
Many such cases. Also fuck you retard lol

>>16837888
>>16837966
>>16837999
>>16838007
>>16838011
This dude rolls.