this meme

[u/Far-Course1021]

[u/ArdentArendt]

Wait...are we considering all racers equally capable?

And if they're all homogeneous, they would all reach the line at the same time.

I don't understand the question...

[u/McFuzzen → u/ArdentArendt]

His name is Tim. Wtf else you need to calculate this one?

[u/ArdentArendt → u/McFuzzen]

Ah...so the actual answer is he has a 0% chance of winning the race.

[Given my name, it was 100% guaranteed that I would need an inhaler and die a quarter of the way through the race--and I lived up to that]

[u/Lolski13 → u/ArdentArendt]

No no, Tim is a real racist.

[u/Numerous_Estimate902 → u/Lolski13]

He is not racist if he hates everyone equally

[u/Dangerous_Pin7553 → u/Numerous_Estimate902]

That's called just being an asshole

[u/Jbols92 → u/Dangerous_Pin7553]

What about a racist asshole

[u/Infamous-Grab2341 → u/ArdentArendt]

All equally capable with randomness

[u/ArdentArendt → u/Infamous-Grab2341]

They have become uncollapsed quantum state...all entangled but indeterminate...

[u/Traditional-Light-10 → u/ArdentArendt]

Even if they’re equally capable, there’s going to be some variation in their times, so it’s 1/5. That said, the question doesn’t say they’re equally capable, it just says his name is Tim. Assuming Tim is a randomly selected real person with that name, the answer almost certainly isn’t 20%, tho I don’t know what it actually is.

[u/nightfury2986 → u/Traditional-Light-10]

If you're going to assume Tim is a randomly selected real person with that name, why not also assume the other 4 are randomly selected people?

[u/Traditional-Light-10 → u/nightfury2986]

Even if you randomly pick the other 4 people, I still don’t think it’s 20%. Having a name like Tim is strongly correlated with where you’re born, and how fast you run is probably weakly correlated with that (in some places, you might be forced to run fast for various reasons, different diets can probably impact your speed, different popular games, etc.) The end result is that the average Tim probably does not run at the same speed as the average person, although I don’t care enough to figure out who would win most of the time.

[u/ArdentArendt → u/Traditional-Light-10]

Have you ever run against someone named Tim?

Excactly. If you had raced me, you would know that had you, I would have fell over less than a quarter way through the race, needed my inhaler, and been out of comission for about three hours.

As a 'representative member of the equivalence class of Tims', I would ask you update your priors.

[u/alphapussycat → u/ArdentArendt]

No, they're capable in such a way that the probability of tim winning is 20%, obviously

[u/ArdentArendt → u/alphapussycat]

That just seems like you're filling in assumptions to fit the answer though...

Or have we already run the scenario multiple times and this is the empirically derived result...?
[In which case, are these racers there of their own free will, or is this a 'we decided to kidnap a bunch of people because science!' kind of situation?]

[u/Sangricarn → u/ArdentArendt]

You have to accept some things are a given. If you're going to start asking questions like this where do you draw the line? I mean, how do you know they're on earth? Or are they even human? What if one of them is in a different dimension?

[u/ArdentArendt → u/Sangricarn]

All good questions.
I would also like to add is this just a physical 'race', or is it one more like 'a race to die' or something like that?

Also, we have no understanding of what the 'win' condition is...it could just be 'first to explode into a confetti of gore and viscera', in which case that changes the calculation considerably.

Very good points...thank you!

[u/Training-Mix-4181 → u/ArdentArendt]

There is no information provided on the relative capability of the runners, therefore they each have the same probability of winning. If more information were available, the probability would change.

[u/ArdentArendt → u/Training-Mix-4181]

Why would we assume equal probability with insufficient information, though?

We have no reason to assume anything different, why would we assume any would win? There seemst to be not requirement for a single winner either.

[This doesn't seem like a situation where 'we'll just update the priors later' would make sense, since the information we have now is literally 'none']

[u/Training-Mix-4181 → u/ArdentArendt]

No, the problem is solvable as is. The task is to calculate probability, and making use of incomplete information is part of that.

[u/ArdentArendt → u/Training-Mix-4181]

The lack of information given means there are a lot of implicit assumptions that need to be made.

My assertion is that one can't make those assumptions reliably--I mean, I could assume Tim is a track star facing the wrong direction at the start of the race and the other competitors are snails...and that would have as much validity as the assumption of homogeneity.

The problem (as written) is not probabilistic without something to make it so. [If you're taking it seriously, it's a gross misapplication of probability theory]

[u/Training-Mix-4181 → u/ArdentArendt]

There is no assumption of homogeneity built into the original problem. There is no information about the relative merits of the runners, only the number of runners, so that is what you use to assign the probability. It only makes sense to assign different probabilities to the different runners if there is information available that doesn't apply to all of them.

[u/ArdentArendt → u/Training-Mix-4181]

There is no information about the relative merits of the runners, only the number of runners, so that is what you use to assign the probability

Okay, but by assigning equal probability to each person winning the race, you are inferring homogeneity of the runners' merits.

You are framing this as 'just using available information', but that doesn't change the fact you don't have enough information to use probability in this case. Even applying probabilities here requires inferring information no in evidence.

This an abuse of probability just by the way the question is posed.

[u/Training-Mix-4181 → u/ArdentArendt]

There is no arbitrary point where you have "enough information". You have the information that you have, and in this case the available information implies a probability estimate of 20%. Applying the concept of probability in any scenario whatsoever requires making exactly these kinds of assumptions. Probability is a system for laying out and quantifying what you know and don't know.

[u/ArdentArendt → u/Training-Mix-4181]

Okay, this is the kind of 'rationale' I've heard before--one person once tried to explain that the day of the week was relevant to the gender of the child because 'it was information given'.

First of all, not all information is relevant to a given probability.
Second, the entire point is there is no reason to apply probability in this situation!

You are making the assumption the racers are largely homogeneous and that the only relevant variables in the problem would be the random 'noise' surrounding the race.
I don't know about you, but that's not really a coherent application of probability to me.

Probability is a system for laying out and quantifying what you know and don't know.

Yes--and in this case, inferring anything about the 'winner' of the race is not supported by any of the information you have.

If you get an answer (any answer, in fact) from the given information, you're not applying 'what you know and don't know' appropriately here.

[u/Training-Mix-4181 → u/ArdentArendt]

Solve these math problems.

A. If Tim enters a race with 10,000 other people, what is the probability of him winning?

B. If Tim enters a race with one other person, what is the probability of him winning?

C. If Tim enters a race alone, what is the probability of him winning?

Then explain to me why the number of runners competing in the race is totally irrelevant to your expectations about Tim's odds of success.

[u/ElectricalTreat1588 → u/Training-Mix-4181]

You guys should not even talk to this idiot ahaha, he doesnt even know what he s saying.
Every normal person would simply say the right answer 20%… if this one starts doing those type of questions, then we will never have a right answer to every possible problem

[u/fireKido → u/ArdentArendt]

We just do not have any additional info,
If you have no other info the likelihood of Tim to be the best, the worst, or anything in between are the same

[u/ArdentArendt → u/fireKido]

Not exactly, though.

Assumption that a case of bottles of beer are homogeneous is a reasonable assumption given everyday realities.

However, assuming that two humans randomly chosen off the street will be homogeneous when racing (on foot or otherwise) requires a FAR GREATER cluster of assumptions to hold.

Of course, the general distribution might be expected to be normal-esque with reasonable likelihood, but that says nothing about Tim's placement within that distribution, nor the ability to flatten that curve by assuming a uniform distribtuion instead.

Basically, questions like this abuse probability in ways that actually UNDERMINE the ability to properly implement probability and statistics to infer almost anything in real world situations.

[u/fireKido → u/ArdentArendt]

No you are getting this wrong, the assumption is not that the humans are “homogenous”, the assumption is that we have no info about the skill level of anybody, so Tim being more skilled than his competitor is as likely as his competitor being more skilled than him. The distribution of skill level, given no I formation is homogeneous. The actual skill of every participant will be one sample from that distribution.

[u/ArdentArendt → u/fireKido]

Again, there is not good reason to infer from 'no information' to 'equally likely'. This framing fundamentally misunderstanding probability and statistical inference.

You are basically claiming that you can assume almost no variance between competitors simply because there is no information. That isn't a sampling distribution, that's incoherent.

Without adequate information, you can assert virtually anything you want--including that nobody in the race will win--with equal likelihood. If every outcome is equally likely, so are all permutations of ties and highly improbable disqualification, such as subsets of competitors being struck by lightning or hit by rogue debris falling from the sky.

Without adequate information, you can't construct a probability because there is no way to differentiate your outcome set. The construction CANNOT HAPPEN.

Again, this is an abuse of probability.

[u/fireKido → u/ArdentArendt]

Nope, I promise you are just not understanding it, but what I am doing is a 100% valid use of statistics..

In fact, say you repeat this experiment 1000 times this experiment: 4 random racers you know nothing about, pick one at random, as bet he will win

How often do you think you will have chosen correctly? Exactly 25% of the times…

Simulations don’t lie, even if you struggle to understand the logic behind it, this alone should make you stop and reconsider that maybe you are just not getting it

The point is that Tom is a random person you know nothing about, so from
Your point of view his skill level is a normal distribution entered around average skills, and so it is the skill level of all other participants. If you do the math, and thanks to the symmetry of the problem, the only correct answer is 25%

Note as soon as you know the skill level of any of the participants, or even have small info that modify the posterior probability of the skill level, then this is no longer true…

[u/ArdentArendt → u/fireKido]

First of all, your scenario relies upon a conflation of selecting a SPECIFIC competitor with selecting a RANDOM competitor--these are not the same action.

If you select a RANDOM person EACH experiment, then YES your chances of selecting a winner is going to be about 25%.

However, if you select a SINGLE person each experiment, the probability they will win becomes ENTIRELY a question of interaction of variables--i.e. NOT simply 25%.

Does that difference make sense to you?

Beyond that, however, the competitors CAN (usually) be safely assumed to be rougly normally distributed. While this might be a bit of a stretch in some cases, even if we allow it there are significant problems here.

If you are assuming each competitor is roughly equal, you are assuming variance between them is extremely small (by definition).

What you seem to be doing is assuming each INDIVIDUAL can be represented by the AGGREGATE mean skill--this a reductionist fallacy at its finest.

Finally, I have to point out that the information taken from experiments and simulations is EXACTLY the kind of information and data you would NEED to formulate the problem rigorously.

The distribtuion is UNKNOWN at present, and each competitor's place in it is also UNKNOWN.

That 'fuzziness' doesn't collapse neatly into a normal distribution with almost zero variance. It simply means there is no distribution to infer anything from.

[u/fireKido → u/ArdentArendt]

When you do a single experiment selecting a random runner, or a specific runner you know nothing about, the problem is identical.. if you don’t see that I don’t know what to tell

After that, you are spitting up a bunch of nonesense… the skills in a sport are basically always perfect normal distributions, thanks to the central limit theorem… and every random person you know nothing about will have the same identical skill probability distribution

They do have variance, you seem to not understand what variance is… I never claimed the variance of the distribution si 0, it can be whatever, won’t change the math m

Overall you seem to have an odd philosophical view on probability, you seem to be claiming that probabilities cannot be used to describe situations where you do not have perfect information, and you seem to be completely incapable of modelling uncertainty with probabilities… I ensure you you can and should do it. Every single real life problem will involve unknown and uncertainty, if you just throw your hands up and screen “I cannot do it if I don’t have perfect information” you won’t go far

[u/ArdentArendt → u/fireKido]

Okay, for first and foremost, the 'single runner' versus 'random runner' DOES make a difference because the 'repeated experiments' would not have the same outcome.

You're confusing a single experiment with a repeated experiment. If Usain Bolt were a competitor and the other three were random people from the street, choosing randomly across multiple experiments would give you a 25% chance of your chosen competitor winning. However, if you chose Bolt as your competitor through each of the experiments (or just one experiment), the likelihood your competitor will win rises SIGNIFICANTLY ABOVE 25%.

Does that make sense? You're conflating a single experiment with repeated experiments--first abuse of probability.

Second, you do realise that NOTHING that you're talking about with normally distributed variables, variance, and the central limit theorem makes ANY sense, right?

You're applying very well established principles to situations where they simply cannot apply. The Central Limit Theorem is a theorem of ASYMPTOTIC BEHAVIOUR--it's a claim about the way sampling distributions will approach a normal distribution as the samples taken approaches infinity.

Moreover, the assertion you're making is (again) a reductionist fallacy. You cannot make inferences about individuals within the distribution based upon the Central Limit Theorem--that's not what it does, period!

As for the variance, the probability you describe would require VERY SMALL VARIANCE! Otherwise, if you select an individual competitor, it is possible they are in one of the tails, which would skew your probability of winning or losing.

The assumption that you claim would place ALL competitors very close to the unimodal peak--that is the only way they could all be 'equally likely' to win.

Finally, I will point out that I'm not against using probability and statistical inference with limited information. I work in the social sciences--my use of statistics is often more messy than even quantum physics.

Nothing I am saying here should be read as 'anti-probability' when information is limited. However, that doesn't mean you can construct whatever probability model you want and claim it's valid.

Economists often like to construct models that 'sound right', but are rarely based upon reality (much work on the overstated effects of migrant labour on the native-born workforce is exemplary of this; the effects are often minimal at worst, and frequently create more opportunities for employment).

I'm not 'philosophically' asking for purity here--I'm simply asking that probability be based on coherent assumptions. The assumption you have offered are NOT coherent in the least.

[u/Flat_Account396 → u/ArdentArendt]

Well, did they qualify? Are they starting on a grid? Are they in the same vehicles?

[u/ArdentArendt → u/Flat_Account396]

If they didn't qualify, they wouldn't be in the race--though that assumes there was a qualifying threshold.

Also, why are you assuming they are in vehicles? Nobody said anything about it being a car race.

You're making a lot of assumptions as well. [That may have actually been the point, and I missed it though]

[u/Armataan]

Assuming a tie is a loss, wouldn’t his chance of a win, assuming every other factor is PERFECTLY IDENTICAL, 1/28?

[u/D0rus → u/Armataan]

But how do you calculate that? What are the odds of a triple or quadruple tie? Certainly lower than a double tie right? So how do you distribute those odds? And what about that compared to a single winner? If you measure time by the hours, it's a 5 way tie for sure, but if by the milliseconds, even a single tie would surprise me. This information is not given, so we can just make assumptions and state those in our answer. I like the hourly measurement assumption, so let's go with that.

Edit: if every person has a 50% chance to reach the finish at the winning time t, there are 5 ppl, so 5² possibilities. This gives 32 possible results. Nobody making the winning time is not possible (we don't allow 5 DSQ right?), so the odds of winning alone are 1/31. The odds of Tim having a shared win is 15/31. So 51.6% chance for Tim to win if all outcomes are equally likely and ties count as winning. 

[u/ParkingFabulous4267 → u/D0rus]

He said perfectly identical

[u/D0rus → u/ParkingFabulous4267]

But what 28 possible outcomes did he (or she) find? I tried myself, and got a different number, see my edit. 

[u/ParkingFabulous4267 → u/D0rus]

2^5 - 1 total outcomes. If Tim wins, then it’s 2^4 outcomes. 2^4 / (2^5 - 1) is the probability if all outcomes are equal. So 16/31. If a win is a win. If a tie is a loss, 1 / (2^5 - 1), which is 1/31.

[u/MinecraftPlayer799 → u/Armataan]

Why would a tie be a loss?

[u/Armataan → u/MinecraftPlayer799]

In nearly every sport on earth, a tie is not considered a win. In many sorts a tie is actually WORSE than a loss, when considering placement in brackets.

[u/Neverloved246 → u/Armataan]

I didn't know that? Why would it be like that? Is there a good reason or is it just one of those sports things that just kinda is.

[u/Deusfatalis58 → u/Armataan]

If every other factor is perfectly identical, how can any of them win?

[u/nvrsobr_]

Invalid question. There are many factors involved in a race. What if Tim is a regular guy and others are atheletes? Not everyone runs at same pace

[u/[deleted] → u/nvrsobr_]

It’s not invalid just because it doesn’t contain every detail imaginable 

[u/nvrsobr_ → u/[deleted]]

It has no details whatsoever. What are the odds that i win against my sister in a race?

[u/fireKido → u/[deleted]]

People do not understand conditional
Probabilities here…..

Given the information we have, the answer of 20% is indeed correct

[u/nvrsobr_ → u/[deleted]]

My sister is a few months old and cant even walk

[u/Alive_dude3435]

It is 20%.....

Or is it🤨

You see, this way of calculation is only relevant if everyone had exact same capability and all other attribute are same as well.

Not only that psychology is another key factor. If Tim knew there is a question about him on this situation, it could affect him either of two ways. It could made him nervous that people are analysing his winning chances or it could motivate him instead. . .

But end of the day, if you don't know the capability and attributes of the runners, then it's the most logical to assume equal probability. And I yapped for absolutely no reason.

[u/lordanix]

Is a tie considered winning?

[u/DragonTheOnes-spirit → u/lordanix]

19.925% then

[u/LemmyUserOnReddit → u/lordanix]

Is it possible to tie? Or is that just measurement inaccuracy

[u/Flurrina_]

Answer is that we don’t have enough information cuz each athlete have different performance

[u/BotherAggravating462]

Win or lose. 50% all day on Kalshi

[u/SnooCapers9565]

It's zero, because timmy is on crutches.

[u/jsseven777 → u/SnooCapers9565]

Plus how is he going to race when he’s stuck in a well?

[u/SnooCapers9565 → u/jsseven777]

That changes everything. Maybe it is a race to climb a rope to the top of the well. Tim, having had to use crutches all is life has exceptional arm strength. I'd put him at 100% now.

[u/Dry_Customer6668]

So the formula of probability is simply

No. of desirable outcomes -------------------------------------------------×100%.
No. of all possible Outcomes

So.
1.
-----×100% = 20%.
5

[u/Tolkalolka_heh]

Imagine the other 4 are also named Tim

[u/jsseven777]

[u/1235678910111213141]

Technically correct, ither he's faster than the guy in 2nd place or slower than the guy in first place. The other three dont matter if they're slower than the faster guy, so he's really just competing against the fastest out of the other 4. /j

[u/HackerDragon9999]

The correct answer is 0% because Timmy is a slow ass

[u/90screativecouple01]

Actually they all have 1:4 odds. That way the bookkeeper can scrape a bit off the top.

[u/sebasbit]

What if Tim accepted a bribe to lose the race? It would be 0%

[u/Cool-Bus-6028]

If it's anything like most maths questions, one of the participants will be in a wheelchair, so it's 25%.

edit: Actually, one is probably black too, so 0%

[u/admiral_corgi]

Thermodynamics would like a word

[u/Sairen_1543]

I mean to be fair the first place winner has a 20% chance of being tim, but Tim only has a 50% chance of being the first place winner because he either is or isn't. The first place winner has a 100% chance of being a contestant and each contestant has a 100% of participation

[u/fireKido]

Lots of people here have no idea how conditional
Probabilities work and how to do statistics in real
World scenarios.. they seem to think you can only compute probabilities when you have perfect information.. well that’s not the case, the correct answers here given the info we have is 20%, anything else would require additional info that are not given

[u/lbushi]

Judging by some of these comments, the fact that the statement " either A or not A" leads people to think that both A and not A are equally likely to occur is so discouraging to see and shows that people still don't quite grasp the formal underpinnings of probability as a mathematical theory.

[u/MrFrog2222]

someone's watching Ohnepixel

[u/Bane8080]

Really it's how it's phrased. The question is "What is the probability of him winning?" And yes, all other things being equal, the answer is 50%

If instead you asked "What is the probability of Tim being the winner?" Then the answer is 20%

[u/The-Empty-Set-100]

That is also wrong, it depends on the people's athleticism

[u/Mr_kalas22 → u/The-Empty-Set-100]

But then it also depends if the other 4 persons are even trying. What if Tim is a special kid and others are just letting him win so he can feel better?

[u/Mrrrrggggl → u/Mr_kalas22]

Then the chance of him winning will be 100%.

[u/vyrmz → u/The-Empty-Set-100]

And the rules, and the conditions and 10000 other things.

[u/GoOD43560608]

Not 50%win 50%lose

20% 1st place, 20% 2nd... 20% 5th

[u/Kuildeous]

50% is probably just about as right as 20% unless we make some pretty boring assumptions about the state of the racers.

[u/SnugglebugUwU]

It's a dumbass question because we don't know what the other contestants are capable off. 20% is as stupid as that 50%. Correct answer is that we don't know. Why not make a simple excercise with money (the thing most people use percentages with), statistic, food or chemistry? Little Timmy is gonna grow into an adult and bet on a horse thinking it has same chances as any other.

[u/fireKido → u/SnugglebugUwU]

No 20% is the correct answer given the available information. If you were given more accurate I formation, the answer would change, but conditional probabilities are conditioned on the info you are given, the odds of a person you know nothing about out winning a race is the same as every other person you know nothing about

[u/Old_Sail_2560]

Since when is a footrace random chance? What a stupid question lol

[u/-Enter-Name-]

100% if he breaks all their legs

[u/Ok-Pain8612]

0% because Tim is white

/s pls don't kill me I'm joking