/sci/ - Science & Math

An infinite amount of steps, since given an ifninite number of tries, there will be an infinite number of instances in which the parameters are met.

>>10033568
Is it zero? The chances of that even happening are so low that its nuts.

>>10033574
uhh false

>>10033568
I think that given an infinite amount of flips, the amount of times it will have landed tails, will be close to 50%, so the scenario where one result will happen 3x more often than the other, will only dwindle with each flip. But brainlet me is not sure if this has anything to do with the law of large numbers.

>>10033637
How is it false?

>>10033651
just false dude, ha ha. try again

>>10033568
In most cases its going to be less than ten steps. I am having a hard time trying to find the function that governs this because I am wondering about smaller multiples like 1.1x or less.

>>10033568
He can never stop flipping the coin so it never lands, meaning he doesn't take any steps?

>>10033568
five

>>10033568
Tricky question, but rather interesting
The man will take an infinite amount of steps given a non-infinitesimal chance that out of 4 consecutive flips, at least 3 will be heads in a recurring fashion
The chance is non-0, but it's rather low and it's the extreme case of the scenario
Not taking any steps is the same non-0 chance, but statistically more likely, using a fair coin

>>10033568
>After each flip, if the number of times the coin has landed heads is three times larger than the number of times it has landed tails, he takes one step forward.
that doesn't make sense, there's no way for the number of times heads lands to be greater than three after each individual flip.
0 is the answer.

>>10033568
Lmao l’hopitals

>>10033673
Why? Number of times the coin has landed on heads can be greater than 3 if it has landed on heads in the past

>>10033673
I noticed the poster count didn't rise when you posted this. It seems you've given up on answering the question and have begun trying to convince yourself it is a trick question. It's not. It's actually pretty straightforward.

>>10033677
it can't be larger than 3 after each individual flip.
It can only land heads or tails once, right?
>>10033679
I'm not OP, I'm actually some anon that is shit at maths but likes fun word games.
Since you find it pretty straightforward, would you mind explaining it?

>>10033680
If I flip a coin three times and it lands on heads all three times, what's the number of times the coin has landed on heads?

>>10033686
Depending on the age of the coin it could have happened hundreds or thousands of times

>>10033690
So you admit it's greater than 3?

>>10033686
>If I flip a coin three times and it lands on heads all three times, what's the number of times the coin has landed on heads?
You're right, the cumulative amount is 3.
But how many times did it land on heads after EACH flip?
The "A man flips a coin an infinite number of times" part in OP seems like a bit of a red herring.

>>10033695
So how many times has the coin landed on heads after the 3rd flip? You seem to struggle with basic English

>>10033699
>So how many times has the coin landed on heads after the 3rd flip?
Depends, the word "each" implies a reset to whatever we're keeping count of, no?

>>10033705
>>10033699
Maybe I'm being a bit autistic about how the OP is written, but then again, maybe I'm not.

>>10033705
No
>>10033707
You're not autistic, you're just a retard who doesn't understand English

>>10033679
So what's the answer?

>>10033711
>You're not autistic, you're just a retard who doesn't understand English
Ok, can you stop wasting time with me, El retardo, and post the answer?

>A man flips a coin an infinite number of times. After each flip, if the number of times the coin has landed heads is three times larger than the number of times it has landed tails, he takes one step forward.
let h be the number of times the coin has landed on heads
let n be the total number of flips
let s be the number of steps
if [math]\frac{h}{n-h} = 3[/math] a step is taken, therefore, the question is how many times will [math]\frac{h}{n-h} = 3[/math] as n approaches infinity?
So what is the chance of this being true after any given n?
(To Be Continued)

Is OP asking for the expected value of the number of steps the man will take in that scenario?
Or is he asking for the probability density function of the random variable for the number of steps taken in the OP's scenario?


>>10033654
much less than 10. we will actually converge to the answer pretty quickly just by looking at all possible coin strings of length 4N with progressively larger n and counting how many of them will have heads :tails in ratio 3:1 compared with coin strings that don't satisfy that.
the contributions of long coin strings to the overall expectation value will quickly become tiny.

so for strings of length 4 there are 16 possible strings, 4 of which satisfy the 3:1 ratio, the expected number of steps taken forward is 0.25

for strings of length 8 , there are 256 possible strings , a quarter of which the coins landed in a 3:1 ratio after the 4th coin toss. Of those, again a quarter will land in a 3:1 ratio. so these circumstances contribute 1/16 *2 and 3/16*1
Of the remaining 3/4 of the strings that didn't take a step after the 4th flip we require that after 8 flips they divide in a 3:1 ratio and that both the tails are either the first 4 or the last 4 flips.
there are 256 strings of length 8 of which 8C2 = 28 are in a 3:1 ratio and 12 of those meet our requirements to prevent double-counting.
so the expected value of steps taken after the string is 8 flips long is 1/16*2 +3/16*1 + 12/256*1 = 0.359

so we added less than to the expectation value of just considering strings of length 4.
considering that the contributions of longer stirngs will get smaller and smaller monotonically , we can therefore bound the expectation value as less than the infinite series of geometric series with starting value 0.25 and ratio 0.5 ,

so the expected number of steps taken will be less than 0.5

>>10033725
Write out the expected value for n flips, then take the limits as n goes to infinity

>>10033732
>>10033735
3 times larger does not mean 3 times as much

>>10033735
*we increased the expected value by considering strings of length 8 by less than half what we got by considering strings of length 4.

Maybe a couple steps in the beginning then none ever again

>>10033732
>>10033735
No.

>>10033739
no, that's exactly what it means.

>After each flip, if the number of times the coin has landed heads is three times larger than the number of times it has landed tails,

i.e.
1H1T don't step
2H1T don't step
3H1T number of heads is 3 times larger than number of tails so step
4H1T number of heads is 4 times larger than number of tails not 3 times larger than the number of tails so don't step

You're claiming that the OP actually said
>After each flip, if the number of times the coin has landed heads is greater than or equal to three times larger than the number of times it has landed tails,
in which case the behaviour would be
1H1T don't step
2H1T dpn't step
3H1T number of heads is equal to 3 times larger than number of tails so step
4H1T number of heads is greater than 3 times larger than number of tails so step

But the OP did not write that.

>>10033760
>You're claiming that the OP actually said
>>>After each flip, if the number of times the coin has landed heads is greater than or equal to three times larger than the number of times it has landed tails.
I didn't claim that, retard. 3 times larger means 4 times as much. 3 is not 3 times larger than 1, it's 2 times larger because 3 is larger than 1 by 2, which is 2 times 1

>>10033765
This, I was literally typing the same thing

I doubt it's going to have a smart, analytical, precise answer unless the question can be re-posed as a markhov chain or a recurrence relationship and I don't think it can .

>>10033765
please don't misuse the english language. You're simply wrong.

the number 3 is 3 times larger than the number 1. the number 4 is not 3 times larger than the number 1.
you can say that the number 4 is >3 times larger than the number 1 , but the number 4 is not 3 times larger than the number 1.

study a little harder in your ESL lessons.

>>10033653
oh thx makes sense now

>>10033665
/thread

>>10033765
>3 is not 3 times larger than 1, it's 2 times larger because 3 is larger than 1 by 2,
you and >>10033769
should both kill yourselves for this retardation.

>>10033735
This is literally so fucking retarded, it is expressly impossible for the man to take 0.5 steps

>>10033785

>>10033792
Wow, you really showed me!

>>10033568
>If you roll a dice how many dots will show?

>>10033779
>>10033784
3 is times as large as 1, not 3 times larger than 1. What number is 0 times LARGER than 1? What percentage is 0% LARGER than 40%? You're the one who doesn't understand English

>>10033797
Expected number of dicks a random human has: 0.5

>but dats impobible!!!!111

>>10033779
>>10033784
3 is 3 times as large as 1, not 3 times larger than 1. What number is 0 times LARGER than 1? What percentage is 0% LARGER than 40%? You're the one who doesn't understand English

>>10033779
What number is 3 times lesser than 1, ESL nigger?

>>10033805
The OP specifically asked how many steps the man takes. Not the "average number of steps a million people running the experiment would take"

>>10033735
The expected number would be the probability times the number of trials and since you are multiplying by a infinite number of trials then the number of steps would be infinite too.

>>10033819
Then there is no answer you stupid fuck, it could literally be any amount and there is nothing mathematically interesting about the question. Or you could interpret the question correctly and stop being such a fag.

>>10033820
No, it's the limit as the number of trials approaches infinity. Stop posting on the math board.

>>10033830
This is a /sci/ence board, math was just an afterthought

>>10033653
infallible logic

>>10033837
Well I don't see any science in your posts, just bad math.

>>10033568
There's a non zero probability that the coin lands on heads every time.

Therefore, the man can potentially take an infinite number of steps.

>>10033799
wow, nice roll.

>>10033882
There is 0 probability that the coin lands heads everytime as number of flips goes to infinity, brainlet. He can potentially take infinity steps, but that's also not what the question is asking. He can potentially take any number of steps

>>10033882
There is 0 probability that the coin lands heads everytime as number of flips goes to infinity, brainlet. He can potentially take infinite steps, but that's not what the question is asking. Also, he can potentially take any number of steps

>>10033568
Twice. Maybe thrice. Maybe frice.

>>10033568
What ever outcome of flips the man gets obviously

>>10033895
>Maybe frice.
frice, farce, thrice.

>>10033894
>There is 0 probability that the coin lands heads everytime as number of flips goes to infinity, brainlet
*sigh*
Ok, there's a non zero probability that the number of heads is a million times greater than the number of tails. Happy now, faggot? Kill yourself.

>>10033568
well definitely more than one quarter of a step, and definitely less than one half of a step.

You can write a program, that, can use registers to keep track of the number of flips, outcomes and weights of each outcome, and give you a naumber after each particular number of flips.

sadly this shit is like: how many occasions of two heads and six tails, and

hey we are free of subtracting duplicates, because duplicates are weighted multiple times, so the answer is (N goes from one to the desired number of flips divided by four (4n! / (n!*3n!)) / (2^4n)

Now, this shit is not correct, beacause, if the number of flips is not divisible by four, there are extra flips that create bad cases, and those need to be adressed in the denominator, but provide no extra good results.

Matlab will create you a lovely graph taht has jumps at every fourth coin flip, flatlines leading up to the next.

Damn, i just might download octave for this.

now, if only n could go to infinity

>>10033911
It's still not relevant to the question. And 0 probability doesn't mean impossible

>>10033925
'0 probability' does mean impossible, in the case of your life amounting to anything meaningful.

>>10033933
What is the probability of getting 0.5 from a uniform distribution of [0,1]?

I think because of the nature of infinity it is infinity. You get tricked by the law of large numbers that says as the number of flips gets very large, it gets very unlikely that the ratio of h/t is far from 1, BUT it's never zero so infinite flips eventually the criteria occurs infinite times. Think about, you've done a million flips and there's been about 1/2mil H, 1/2 mil T. Can you then get a run of 1 million H? Yes.
Either this or i'm getting fucked by the probability getting small faster than the flips get large and i'm supposed to take a limit which turns out to converge

>>10033933
You are so dumb

>>10033941
Please don't be mean, friend

Infinity is not real. There are maximums and minimums to everything.

>>10033972
it's a conceptual tool. Your comment is irrelevant. your life is irrelevant

>>10033974
It is not a useful concept. You're retarded.

>>10033972
>There are maximums and minimums to everything.
prove it.

>>10033972
What is the maximum natural number?

>>10033568
(infinite steps)-1

The man can only take steps on flips that are multiples of four. The odds of doing so are [math] \frac{\binom{4n}{n}}{2^{4n}} [/math]. So the answer is [math] \sum\limits_{n=1}^{\infty}\frac{\binom{4n}{n}}{2^{4n}} [/math], which appears to converge to a bit more than 0.47368.

Sorry if formatting is fucked up, phoneposting rn

>>10033980
Speed of light is a maximum.
Particles of matter aren't smaller than electrons.

both are defined by real, finite values.

>>10034004
Should be 5n

>>10033982
There is none, and not having one does nothing to validate the concept of infinity.

Numbers are trivially pointless as abstract self reference. Numbers are meant to be attributed to the real world, like counting.

>>10034024
How many natural numbers are there?

>>10034015
>Speed of light is a maximum.
>Particles of matter aren't smaller than electrons.
just wait for Xenu, bro.

>>10034026
How few brain cells do you have?
May as well be asking me how you can fly by willpower alone. Its in your head.
You're fantasizing.

>>10034019
No.
Out of 2^4 = 16 ways to flip 4 coins, there are 4 choose 1 = 4 ways to flip 3 heads and one tails:
T H H H
H T H H
H H T H
H H H H

>>10034039
3 is not 3 times larger than 1

>>10034026
That is self referential, you are asking for a number to define how many numbers there are

Numbers are used to define how many of other things there are. Using them on eachother is autistic

>>10034026
>How many natural numbers are there?
How many oxygen atoms are there?

more than you can count but definitely not enough to prevent your hypoxia.

The number of steps is the same as the probability of getting r=3(n-r) successes out of n trials as n approaches infinity. Wait is this a contradiction or a paradox or something?

>>10034066
Wrong

>>10034046
Oh shit. Then its about 0.221143

>>10034015
>Particles of matter aren't smaller than electrons.
How would you observe something smaller than an electron when the tech we use to find the smallest thing we use to find said smaller things uses electrons to do so.

So this may be a potential answer to your question.
There was this guy, John Kerrich, WWII POV, that spent his time imprisoned flipping a coin. (not shitting you, he was that bored). He found that the proportion of heads to tails fluctuated wildly the more trials he took (image related).
Basically, when you take more trials in this infinite set of trials, the difference will become greater and greater. Hypothetically speaking, this man in the problem would be able to walk as long as he pleased, but why would he? And why is he holding himself to such asinine restrictions to walking?

>>10034104
Image Source:
https://stats.stackexchange.com/questions/76663/john-kerrich-coin-flip-data

>>10034104
I could write a script to do this in 5 minutes, lel, dont act like thats some sort of scientific discovery

>>10034086
How would you observe electrons. How would you observe atoms. Microscopes cant see atoms.

>>10034114
>minutes

>>10034178
Brings up an interesting point. There are many phenomena only proven to exist after the presupposition that they ought to. Atoms, the speed of light. These might not be as real as once thought.

>>10034197
Proven dumb through demonstrating self fulfilled prophecy baiting.

>>10034203
If you can come up with a theory that rejects all of these things and explains everything better than current theories, be my guest.

Some actual calculations here.
I tried the naive approach of trying to find the number of possibilities.
First the formula for the expected value we want to compute.
Then the probability that he takes k steps within n throws (we take the limit as n goes to infinity).
To get this probability I consider all tuples of distances between throws that make him hit H = 3T and sum over the possible number of paths to connect these (you know you have to go distance to the right and 3/4 distance up so you get some n choose k kinda value.
This leaves me with a clusterfuck formula
(2nd image in reply)

>>10034456

>>10034178
>Microscopes cant see atoms
But they can

>>10034197
Completely meme post

>>10034004
unless there is a floor function and a division by four near to it, the solution is not correct, or is only looking at increments of four.
well guess what, if you do seven flips, the number of possible hits stays the same as at four, but the number of overall possibilities, as the weighing factor goes up drastically.

>>10033568

The question is poorly worded.

You're asking for the expected (or average) number of steps the man will take. He could flip an infinite sequence of tails and never take a single step.

>>10033807
>3 is 3 times as large as 1, not 3 times larger than 1.
those statements are equivalent. Be honest, english is not your first language. Just admit that you made a false assumption.

>What number is 0 times LARGER than 1?
there is no such number. it's invalid to use the construction "x is y times larger than z" when y is less than or equal to 1. The fact that you're saying x is "y times larger" forces y to be a positive number which when multiplied by z results in a number that is more positive than z. hence using the description "larger".
>What percentage is 0% LARGER than 40%?
as explained above
>You're the one who doesn't understand English
Now that I have explained precisely why you are wrong I hope you will have the intellectual integrity to admit that you're wrong instead of wallowing in butthurt.

>>10034004
I didn't realise you'd be able to just add all the possibilities every 4 steps like that. I thought that you'd end up counting the earlier sequences multiple times like that.

>>10034046
yes it literally is you cretin.

>>10034654
>>10034663
ESL nigger

>>10034464
Thats an electron microscope, brainlet

>>10034343
Kill yourself after killing your worthless friends and family.

>>10034654
What does "50% increase" mean to you? What does "100% increase" mean to you?

People are STILL responding to this? It’s a bait question with ridiculous parameters- I would think after posts like >>10033653 you people would have let this nonsense die.

>>10034685
what's ridiculous about the parameters?

>>10034685
How is it ridiculous? Someone already got the correct answer

>>10034688

>>10033972

Let Xn be the random variable that gives 0 if the nth flip is heads, 1 if tails. Assume the coin is fair, i.e. probabilities are both 1/2.

Let Yn be the random variable X1+X2+...+Xn. Yn is a Bernoulli distribution with parameters n and 1/2.

Clearly a step is only possible when the number of flips is a multiple of 4. The man takes a step at the (4n)-th flip iff Y4n=n. The probability of Y4n being n is easily computed using the binomial distribution formula.

The random variable Z that counts how many steps are made is the summation of all the Y4n for n ranging from 1 to infinity. Now the distribution of Z could be computed as a limit of partial sums.

I'm not sure the Y4n variables are indipendent though.

>>10034690
The answer isn't infinity

>>10034691
*Independent ofc

>>10034692
The question isnt valid.

>>10034704
Why not?

>>10034711

>>10033972

>>10034086
>How would you observe something smaller than an electron when the tech we use to find the smallest thing we use to find said smaller things uses electrons to do so.
holy fuck, I need to stop posting when I'm tired; Let me translate my tardspeech in that post:
We use electrons in electron microscopes, would an electron microscope be able to detect anything smaller than an electron?
Is there any tool that can detect anything smaller than an electron?
If no, then how can we be certain that there's nothing smaller than an electron?

>>10034718
The fact that it were easy to view smaller and smaller things until hitting the floor that are electrons.

you can entertain the speed of light can't you? its slow. Its not instantaneous. just like it were easy to view faster and faster things before hitting the ceiling of lightspeed.

>>10033972
what's your mom's weight

>>10033765
>3 is not 3 times larger than 1
>3 * 1 = ????
kek

>>10033785
Next you're gonna tell me you can't do half an A press

>>10033975
have fun proving the rigor of calculus

>>10034104
we're talking about proportional variations, not absolute ones.

>>10034030
How many real numbers exist between 1 and 2

>>10034688
where?

>>10034684
>50% increase
1.5x
>100% increase
2x

>>10034745
Now what is 300% increase?

>>10034745
>>10034748
Brainlet here.
quick question, why is a 50% increase 1.5x instead of 0.5x?
is it because 0 can't be increased or something?

>>10034775
50% is a factor relative to the original amount. Increase means how much greater than the original amount. Taken together, 50% increase means you increase the original amount by 50% of the original amount

>>10033765
Hahaha ha

Why only meme answers that don't even mention random variables are taken seriously

>>10034748
4x
I don't see how that fits into your argument though because something being three times larger is not a 300% increase, it is equal to being 300% as big, which means a 3x increase.

>>10034775
It's 100% and 50% more on top, which means 1.5x.
Multiplying by 0.5 results in a 50% decrease. You need that other 1 to carry over the original value.

>>10034829
What is 50% larger? What is 100% larger?

>>10034603
>He could flip an infinite sequence of tails
False.

>>10034868
So you're just denying the premise?

>>10034869
You do not understand infinity. The man will have exactly as many heads as he has tails when any "infinite" number of flips has been taken

>>10034876
There is no "infinite" number of flips, retard

>>10034835
I already explained what the flaw in your argument is.

>>10034938
What does "50% larger" mean? It's a simple question

>>10033574
false because at number of times gets larger the ratio of h/t becomes arbitrarily close to 0.5. this is a law of small numbers problem

>>10034941
Already stated that '50% larger' means 150% of the original value.
'3 is 3x larger than 1' is a true statement because 3 is 300% the size as 1.
If someone had said 'three is three more than one' then they would be wrong because three more than one is four, not three. However, nobody said this, nor has anyone said any statement equivalent to this in this entire thread. Your misunderstanding of the English language is your problem.
Three is three TIMES larger than one. Three is 200% LARGER than one. Three is equal to 300% the VALUE of one. All of these statements are true. They all say the same thing.

>>10034930
Hence the quotation marks brainlet

>>10033568
Only just noticed this, but he only takes a step if it's exactly heads = 3x tails, not heads > 3x tails?

>>10033568
50%
Either it happens or it doesn't.

It's infinity, but it will be a very very slow walk. The reason is that the person takes discrete steps. At each point there is a non-vanishing probability to take a step forward thus after enough tries it will happen.
Looking at a limit in the probabilities of taking a step forward makes no sense (this will of course be zero for going to infinity, as heads/tails = 1), but at each point one could get (3*tails - heads) heads throws in a row with non-vanishing probability and thus take a step forward.

>>10035244
This

>>10033665
Correct

New rule of the internet:
[math]If infinity is part of the question it is also the answer[/math]

https://gist.github.com/ParrotParrot/79afd86edc611a24af05ac855621b98e

You could also make it in something other than python, but that's really up to you

>>10035338
>1690 steps taken over 1000 trials, maximum of 26 steps taken
So yeah, depends mostly on the coin

The simplistic answer is probably none, maybe a few, never more than a few dozen.

Is it a bet? Odds are in favour the man takes 0 steps.

>>10035244

I disagree. The convergence of all heads and tails is .5. It approaches this by the square root of its variance which changes the more trials you make. Square roots aren't linear.
The question says "if the number of times the coin has landed heads is three times larger than the number of times it has landed tails" This assumes all previous trials are tallied as the experiment continues.

That is a cumulative distribution. The more trials the probability of a variance doesn't change, but the probability of the ratio of variance to trials converges to zero.
So the probability of many tails in a row doesn't change, but the probability of many tails in a row compared to the total trials converges on zero.

>>10035075
>Three is 200% LARGER than one
200% is the same as 2 times

>>10033568
i-in... infinite times??

According to the law of large numbers the ratio of heads over tails in the first n flips converges almost surely to 1/2 for n->infinity, so the propability of taking infinite steps is zero. Stop being stupid. Each number of steps is possible with a certain probability.

>>10033765
Don't let these retards confuse you. You are absolutely right.

>>10035075
>Three is three TIMES larger than one. Three is 200% LARGER than one.
Kek, why are you capitalizing "larger" the second time like you aren't contradicting yourself

>>10033972
Infinity is real but its an arbitary concept
fite me

>>10035751
Make infinity infinite again

>>10034739
Why would I attempt to validate stupid brainlet shit for dumb niggers.

>>10033807
>3 times larger
x*3
>3 times smaller
x/3

>>10033807
nigger

> x = 1
>0% of x = 0
>50% of x = 0.5
>100% of x = 1
>200% of x = 2
>300% of x = 3
>400% of x = 4

> y = 1
>0% of 1 = 1
>50% of 1 = 0.5
>100% of y = 1; z = 1
>200% of z = 2; a = 2
>300% of a = 6; b = 6
>400% of b = 24; c = 24

0% larger than 1 = 1
50% larger than 1 = 1.5
100% larger than 1 = 2
200% larger than 1 = 3
300% larger than 1 = 4
(300% of 1) + 1 = (3) + 1 = 4

>>10035401
Odds on favor of 0? No. After three tosses, it's 50-50 that he takes one step. From then on, he has a chance of stepping, so the odds are in favor of 1 or more steps.

>>10033579
>1 day and 14 hours
yet no reply, How do you feel coming back and seeing this?

>>10035244
It certainly does seem to me that no matter what head/tails ratio is the condition for taking a step forward, it will recur an infinite number of times in an infinitely extended trial. The only thing that changes with the ratio is the slope of convergence toward zero-rate, which is never touched. Yet the flippant "this again" confidence of these comments--

>>10033665
>>10033781
>>10035285

nags me into doubt about that, though that answer may itself be a meme I don't know.

>>10033568
As many steps it takes to hit the wall.

>>10033579
>>10036637
It's actually fairly close to being correct

Brainlets.

Let TH = Total heads flipped
Let TT = Total tails flipped
Let n = repetition of coin flip

To take a step
TH = 3TT for n > 3

At n=3
If TT is 0, then one step can be taken at TH = 3.

To solve this you have to sum the probability of TH = 3TT for every n as it approaches infinity. This will lead to a convergance to a finite #, because the probability gets smaller every n.

At n = 1,2. No steps can be taken.
At n = 3 the chance for a step is 0.5^3.
At n = 4 the chance is thhh + hthh + hhth + hhht. This is 0.5^4 x 4
At n = 5,6,7 the chance is 0.
At n = 8 the chance 0.5^8 × 28
At n = 12 the chance is 0.5^12 × (all combinations of 3t9heads)
At n = 16 and so on.

Answer is about .35 steps.

>>10039640
Forgot to add .5^3, so answer is about .5 or 1/2 steps.

>>10039640
Oh and for brainlets you need a ratio of 1tail:3heads. So 2:6, 3:9, 4:12, etc. That is why only every 4 flips matters. Remember the question states heads is 3x larger than tails. 3x larger is the ratio 1tails:3heads.

The special case is at 3 flips because 0:3 ratio for all intents and purposes is 3x larger. Kinda like how 0! is 1.

>>10036637
>throw coin 4 times
>get 3 heads 1 tail
>take a step

Wow yeah literally impossible

Start studying some actual probability theory before trying to solve probability problems you fuckin brainlets

>>10033568
>How many steps will the man take?
at least 57

>>10034748
>>10034835
The question did not say "300% larger" it said
> if the number of times the coin has landed heads is three times larger than the number of times it has landed tails,


"3 times larger" has a totally different meaning from "300% larger". 3 times larger explicitly denotes a multiplicative comparison. That is what times means. hence the meaning of times tables.
if number of heads H is 3 times larger than number of tales T then that means H = 3T

You are confused because you think that "3 tmes larger" actually means "300% larger" but it does not.

>>10035514
he isn't the contradicting yourself. You're the person with a sub-par grasp of english who cannot recognise the meaning of "times" and believes that "times larger" means the same thing as "larger".

>>10039640
>Let TH = Total heads flipped
>Let TT = Total tails flipped
I'm not going to read anything with such a brainlet choice of notation.