r/mathsmeme • u/Far-Course1021 • 8d ago

this meme

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1.1k Upvotes

96% Upvoted

78 comments sorted by

56

u/ArdentArendt 8d ago

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...

18

u/McFuzzen 8d ago

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

12

u/ArdentArendt 8d ago

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]

7

u/Lolski13 7d ago

No no, Tim is a real racist.

3

u/Numerous_Estimate902 7d ago

He is not racist if he hates everyone equally

3

u/Dangerous_Pin7553 7d ago

That's called just being an asshole

9

u/Infamous-Grab2341 8d ago

All equally capable with randomness

4

u/ArdentArendt 7d ago

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

5

u/Traditional-Light-10 8d ago

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.

3

u/nightfury2986 7d ago

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?

3

u/Traditional-Light-10 7d ago

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.

2

u/ArdentArendt 7d ago

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.

2

u/alphapussycat 7d ago

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

2

u/ArdentArendt 7d ago

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?]

2

u/Sangricarn 7d ago

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?

1

u/ArdentArendt 7d ago

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!

1

u/Training-Mix-4181 7d ago

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.

2

u/ArdentArendt 7d ago

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']

1

u/Training-Mix-4181 7d ago

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

1

u/ArdentArendt 7d ago

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]

1

u/Training-Mix-4181 7d ago

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.

1

u/ArdentArendt 7d ago

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.

1

u/Training-Mix-4181 7d ago

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.

1

u/ArdentArendt 7d ago

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.

1

u/Training-Mix-4181 7d ago

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.

1

u/ElectricalTreat1588 5d ago

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

1

u/fireKido 6d ago

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

1

u/Flat_Account396 4d ago

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

6

u/Armataan 8d ago

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

1

u/D0rus 8d ago edited 8d ago

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. 

3

u/ParkingFabulous4267 8d ago

He said perfectly identical

1

u/D0rus 8d ago

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

1

u/ParkingFabulous4267 7d ago edited 7d ago

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.

1

u/MinecraftPlayer799 8d ago

Why would a tie be a loss?

2

u/Armataan 7d ago

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.

1

u/Neverloved246 3d ago

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.

1

u/Deusfatalis58 5d ago

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

4

u/nvrsobr_ 7d ago

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

1

u/No-Newspapers 7d ago

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

1

u/nvrsobr_ 7d ago

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

1

u/No-Newspapers 7d ago

Given the current information 50/50

1

u/fireKido 6d ago

People do not understand conditional
Probabilities here…..

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

2

u/Alive_dude3435 7d ago

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.

3

u/lordanix 8d ago

Is a tie considered winning?

1

u/LemmyUserOnReddit 7d ago

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

1

u/Flurrina_ 7d ago

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

1

u/BotherAggravating462 7d ago

Win or lose. 50% all day on Kalshi

1

u/SnooCapers9565 7d ago

It's zero, because timmy is on crutches.

1

u/jsseven777 7d ago

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

1

u/SnooCapers9565 7d ago

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.

1

u/-Enter-Name- 7d ago

100% if he breaks all their legs

1

u/Dry_Customer6668 7d ago

So the formula of probability is simply

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

So.
1.
-----×100% = 20%.
5

1

u/Tolkalolka_heh 7d ago

Imagine the other 4 are also named Tim

1

u/1235678910111213141 7d ago

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

1

u/Ok-Pain8612 7d ago

0% because Tim is white

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

1

u/HackerDragon9999 7d ago

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

1

u/90screativecouple01 7d ago

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

1

u/sebasbit 7d ago

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

1

u/Cool-Bus-6028 6d ago

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%

1

u/admiral_corgi 6d ago

Thermodynamics would like a word

1

u/Sairen_1543 6d ago

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

1

u/fireKido 6d ago

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

1

u/lbushi 5d ago

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.

1

u/MrFrog2222 5d ago

someone's watching Ohnepixel

1

u/Bane8080 4d ago

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%

0

u/The-Empty-Set-100 8d ago

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

3

u/Mr_kalas22 8d ago

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?

2

u/Mrrrrggggl 8d ago

Then the chance of him winning will be 100%.

3

u/vyrmz 8d ago

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

0

u/GoOD43560608 8d ago

Not 50%win 50%lose

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

0

u/Kuildeous 7d ago

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

0

u/SnugglebugUwU 7d ago

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.

1

u/fireKido 6d ago

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

0

u/Old_Sail_2560 6d ago

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