My 7th grader refuses to put "50%" as the answer here because it's "not how my teacher taught us" and I won't tell him what 63/90 is as a percent as a matter of principle against a poorly worded question! (It should say "flipped an uneven coin" or "experimental probability")

[u/gailonmiles]

No matter how many times it landed on heads previously, the theoretical probability of the next flip is still 50%

[u/Alfredos_Pizza_Cafe_]

Reading this as a neutral party, I would think it's a trick question where the correct answer is really 50%. It should read "what percentage of flips came out heads" if they want a 70% answer

[u/Dry-Manufacturer7761 → u/Alfredos_Pizza_Cafe_]

This. It isn’t a math question, but a “learn to do word problems and remove extra information to answer the actual question.”

[u/ga239577 → u/Dry-Manufacturer7761]

I would agree assuming that is part of what’s being taught in the class. As worded, the answer is 50% … but if the class hasn’t been teaching kids to remove irrelevant information from the question, then the answer they’re looking for is probably 70%

[u/Dry-Manufacturer7761 → u/ga239577]

This is obviously second grade stuff. Logic should 100% be a part of the curriculum by this point. 2nd grade logic is all about saying “too much info, but here is the answer” or “not enough data and I cannot answer”.

[u/Wild-Guarantee-7357 → u/Dry-Manufacturer7761]

Seventh grade, not second grade. 7th graders should know that a coin is 50/50 no matter what

Edit: Everyone is missing the point of my comment again. OP’s child is in 7th grade, not 2nd. That is truly all I meant to say. I used “50/50 no matter what” as a shorthand for the fact that a 7th grader should understand these concepts, along with the nuance that comes along with them.

[u/Rattus375 → u/Wild-Guarantee-7357]

The odds of a 50-50 coin flipping heads 63 or more times in 90 flips is 1/10k. Odds are, this isn't a fair coin

[u/EmberOne1 → u/Rattus375]

But that's the cool thing about probability. Just because it only happens about 1 in 10k times doesn't mean it can't happen the first time, then the 9th time, then not again for 20k times. This has real world implications, too. Take, for example, when a supposed 100 year flood happens, and nobody decides to change any infrastructure to protect against damage or risk to lives next time, because they wrongfully assume that means it also won't happen again for another 100 years.

[u/ga239577 → u/Dry-Manufacturer7761]

My point is the answer the teacher likely considers “correct” depends on exactly what lesson or chapter they’ve been teaching. We all know the right answer is 50%.

The question is worded poorly - because unless there was added context in the teacher’s lessons - it appears the answer they’re expecting is 70%.

This leaves the student in a position where they have to guess which answer the teacher is expecting.

[u/GreatScottCreates → u/ga239577]

> This leaves the student in a position where they have to guess which answer the teacher is expecting.

Not to sound like a smart ass, but I feel like this sentence encapsulates my grade school experience

[u/ga239577 → u/GreatScottCreates]

I had to do this on some CompTIA exams for my Bachelor’s degree so it’s not just grade school.

Multiple questions were worded in a way where the right answer was dependent on the intent of the person asking the question.

[u/DesignerPangolin → u/Dry-Manufacturer7761]

Putting aside that this is a poorly-posed question, learning to translate a natural language question into a formally rigorous mathematical expression is easily the most important part of mathematics education (at least until you get to real analysis). The rest is just mechanical data processing.

[u/Venusgate → u/Dry-Manufacturer7761]

It's not that either, it's a "how to argue with someone that gives you arbitrary data."

[u/Thumbframe → u/Dry-Manufacturer7761]

Maybe they wanted the 7th grader to set up and solve a maximum likelihood equation?

[u/philosifer → u/Alfredos_Pizza_Cafe_]

Technically if we are getting really pedantic, the question never states the coin is fair. It could be a 70% weighted coin

[u/IBetThisIsTakenToo → u/philosifer]

Well, in that case 90 tosses is orders of magnitude less than would be needed to determine that.

[u/FiggsMcDuff1 → u/philosifer]

I did poorly on a lot of homework by stating more information is required because of things like that. I wasn't trying to be an ass either, I just sort of missed the intent of the question.

[u/Lv_InSaNe_vL → u/FiggsMcDuff1]

That is the point of these kinds of questions. They aren't teaching you to do math, they are teaching you to operate with unclear instructions which is pretty common in the real world.

[u/Best-Treacle-9880 → u/Lv_InSaNe_vL]

The answer in the real world is to follow up with more questions though, not just take a guess and hope you've interpreted right. So this is low quality testing

[u/thomsenite256 → u/Alfredos_Pizza_Cafe_]

put 50 and fight with the teacher when its marked wrong would be my answer

[u/Enigma_Stasis → u/thomsenite256]

https://giphy.com/gifs/c9tVMERePnnDW

[u/TheGrandWhatever → u/Enigma_Stasis]

Education sponsored by Kalshi. Is the coin flip odds 70%? Let's bet on it

[u/RandomWordCombo9632 → u/thomsenite256]

Careful. You might get the teacher, the principal and the school district to declare that the odds for heads when flipping a coin is actually 70%

Just like how fire produces wood and oxygen.

for context:

In Firewood combustion:

1. Which of the following statements is correct?
   

a. The cellulose and oxygen products indicate that this combustion reaction is endothermic.

b. The heat and light products indicate that this combustion reaction is exothermic.

c. The cellulose and oxygen products indicate that this combustion reaction is exothermic.

d. The heat and light products indicate that this combustion reaction is endothermic.

Clearly A and D are false. It says endothermic, meaning it pulls in heat.

C is obviously incorrect. Cellulose and oxygen are consumed not produced during combustion.

The answer is B!

Teacher: No. The answer is C because light is not always a result of combustion.

??????????????????????????????????????

And cellulose and oxygen are?!

Not only did the teacher double down when the parents protested, the principal triple downed by backing the teacher. And the school district quadrupled down by stating the teacher was correct in their grading.

It took regional headlines to make them reverse the decision and regrade.

Never underestimate people's ability to be really stupid.

[u/CallMeRudiger → u/RandomWordCombo9632]

The story drew international attention to the district, with emails sent from chemistry experts from several countries, former and current teachers, parents and at least one cannabis business owner who called the teacher’s combustion answer “incontrovertibly false” and the length of the district’s investigation “embarrassing.”

Man am I glad they made sure to include all of the combustion experts who reached out.

[u/RandomWordCombo9632 → u/CallMeRudiger]

Hey man... you gotta know how things work to get the good good ya knwo?

[u/_______no-------name → u/RandomWordCombo9632]

Wow, that is some next level self-fellatio shit. I am glad I have never met profs as dumb and egotistical as that.

[u/doesntbite_much → u/Alfredos_Pizza_Cafe_]

https://giphy.com/gifs/2sddZ3k7yxiVWpFdH3

[u/JHtotheRT → u/Alfredos_Pizza_Cafe_]

In math, you often specify the coin is fair, you don’t just assume it. ‘Sofia slipped a fair coin’ would be the wording to avoid ambiguity. You can’t just assume à coin is fair without that. In fact it’s very likely this coin isn’t fair given the results, but that’s obviously wel outside the scope of a second grade math problem.

[u/MuhfugginSaucera → u/JHtotheRT]

People are getting caught up on the coin part. We should ignore the coin and treat the problem like a math problem. The object is generally irrelevant, the math is not.

The person who wrote this word problem shouldn't have chosen a coin. The world problem and the answer are the same regardless of the object being used.

[u/Sad_Reindeer5108 → u/MuhfugginSaucera]

I'm leaning toward this problem wasn't written by a person.

[u/roosterSause42 → u/Alfredos_Pizza_Cafe_]

That’s the way I read it too.

It’s a lesson in recognizing irrelevant information.

The only info needed is the question “What is the probability of landing in heads” and that a coin has 2 sides, heads and tails.

Ignoring landing on edge and the bias of a flipped coin to result in the side that was up when flipped: the answer is 50%

[u/TisBeTheFuk → u/Alfredos_Pizza_Cafe_]

Knowing this is a 7th grade school question, I think the expected answer here is 70%.

[u/LoudandQuiet47 → u/Alfredos_Pizza_Cafe_]

Well, the way I see it, the problem does not say it's a fair coin. It's a cheat. They want to know if it's a cheat.

[u/pnoodl3s → u/LoudandQuiet47]

But then if its a cheat coin, the chance still might not be 63/90 given the facts, unless we flip an infinite number of times and aggregate all of it to get the exact probability

[u/LazerWolfe53 → u/pnoodl3s]

Yeah, now we're getting into z factors and all sorts of fun stuff. You can provide a tolerance within three sigmas/standard deviations, but you cannot give a definitive answer about the probability of flipping a heads based on the available data assuming it isn't 50/50.

[u/Burger_Queeph → u/Alfredos_Pizza_Cafe_]

It really depends how clever the teacher is. Some teachers think they're the center of the universe and what they meant to ask is just as good as what they actually wrote down. It could be either case.

[u/Rukir_Gaming]

"What is the current percentage of heads to tails flipped"

There fixed the prompt

[u/T_RAYRAY → u/Rukir_Gaming]

What is the historical actual result of heads to tails flips for these specific 90 coin flips.

[u/ganbramor → u/Rukir_Gaming]

“Percentage of heads out of all flips.” If you’re going to say “to” then it’s “ratio of heads TO tails.

[u/DesignerPangolin → u/Rukir_Gaming]

If the coin is fair, the probability of getting a result as or more extreme than 63/90 is p=0.0188, so by the typical statistician's cutoff of alpha=0.05, we'd reject the null hypothesis that the coin was fair and accept that the coin's sampled tilt of 0.7 is an unbiased estimator of the true mean. If you were a particle physicist, you'd accept the null hypothesis as they use a more rigorous standard of five sigma (alpha=2.87*10^-7), so the answer would be 0.5. If you were a parent in whatever state approved this textbook, I would accept the hypothesis that you deserve to be mildly infuriated.

[u/HudeniMFK → u/Rukir_Gaming]

Yes but still no,

[u/BIGBADLENIN]

That has a p-value of 0.0002 given a fair coin, so we can reject the null-hypothesis (the coin is fair) and so our best guess is that that the probability for heads is closer to 63/90

[u/Bad-Luck-Guy]

Unfortunately your kid is probably right, that’s probably the answer to this stupid question. I remember being frustrated by questions like this in school. The one time my Dad tried to help me with math I failed the assignment because he insisted I do everything differently than we were learning in class.

[u/Rough_Possession_ → u/Bad-Luck-Guy]

I had done science homework multiple choice, I asked the student teacher, that was in the same class a clearifing question about one question I couldn't answer. They looked at all my awnsers and made me "correct" half of them. Each correction she provided an explanation that sounded logical but was actually made up. I would have gotten an 87% on that homework but ended up with a 63% the worst part was we spent hours correcting everything because it took me a long time to understand her false explanations. I finally thought I strongly understood the material then I got the grades back

[u/SerendiPetey → u/Bad-Luck-Guy]

My dad used to say: "The coin has no memory." Thus 50/50.

[u/Dontsuemeplsz → u/Bad-Luck-Guy]

I meam its objectively the right choice based on the question. They dont tend to throw trick questions into kids math worksheets, and unless the topic is specifically independent probabilities i dont see it. The 90 flips means it was a sample. The question is asking for the probability of heads in the sample of 90. Not the probability of the next coin being heads, though it is confusingly worded.

[u/Tigglebee → u/Dontsuemeplsz]

If that’s the question you need to say something about the fairness of the coin.

[u/sticky_neutrino → u/Tigglebee]

or even just "based on this sample, what is the measured probability"

[u/TessaFractal → u/Dontsuemeplsz]

I'd always answer questions guessing what sort of answer the teacher expected. And then every so often they would throw in a trick question and it was very irritating.

[u/raz-0]

Your kid has learned the important lesson that you get farther answering the question intended then telling people who can make your life suck that they are morons. The fact they are morons will not help your situation.

[u/RusDaMus → u/raz-0]

You probably meant "than", right? In your version, you're still telling people that they're morons.

[u/rex5k → u/RusDaMus]

Above poster has learned the important lesson that your grammar needs to be perfect if you plan on insulting anyone's intelligence in any way.

[u/Rocket_safety → u/rex5k]

[u/Queasy-Ride4291 → u/raz-0]

You should teach your kid to answer the question as intended, immediately before telling the person that they are a moron. Got it. 

[u/uwill1der]

This is where you learn from your 7th grader the difference between meaning and intention

[u/TealCatto → u/uwill1der]

Are you saying that it's right to reject a very clearly expressed statement and replace it with what you think the speaker actually meant?

[u/ringobob → u/TealCatto]

It's not a statistics class.

[u/BootVillain → u/TealCatto]

And THAT is the typical redditor lmao

[u/TheSpaceNeedle → u/TealCatto]

The curtains were blue

[u/Alex-Murphy → u/TealCatto]

The question isn't in a riddle book. They want you to find the percentage from 63/90, which is 70%.

It's poorly worded but you can easily figure it out if you just use context.

[u/PunchDrunkPrincess → u/Alex-Murphy]

It's not "poorly worded" it's straight up wrong. 50% is the correct answer to the question asked. If they want to know what percentage of flips came up heads then they should ask that. It's not the student's job to assume anything.

[u/ExamplePractical1981]

We had a math test in 7th!!! grade. Our teacher was a douche. The question was about parking a car for 137 minutes and calculating the cost if an hour cost €5. The answer was €15 because every hour started was charged in full. HOW THE FUCK WERE WE SUPPOSED TO KNOW THAT?! We were in 7th grade!!! This shit is STILL fucking me up 20 years later 😂

https://giphy.com/gifs/vmgJEo71lzE85Qy8pe

[u/Ancient_Yellow_709 → u/ExamplePractical1981]

Bro, I had the same type of teacher except they asked how long did some Roman guy lived. I had, of course, memorized the birth and death dates as instructed. I had been studying for the PSAT in 7th grade (there was some reason they had us take it early) and they gave us the tip of not falling for the trick of forgetting inclusive values.

So I think to myself "How many years was he alive? Yeah, that's probably inclusive, right? They didn't ask how old he was when he died, which would require him having completed the birthday cycle for that year so he must be being tricky like that." So I write out the dates I memorized, subtract them, and add one, showing my work.

The teacher marks it fully wrong. I go argue with him, point out that I showed my work and that his question was unclear and point out my logic for answering that way. His answer was that most people answered it correctly and I got a high enough grade already. F you, Mr. B. If you're alive 2000-2010, you're alive in 11 years.

(He also screwed me over in a schoolwide geography bee by assigning the one other girl's mistakes to me and the principal had to intervene; oddly enough, the girl went on to win...the girl's mom worked at the school and he was friends with her.)

Edit: typo

[u/Myclarinetto → u/Ancient_Yellow_709]

But you are wrong tho. He didn't ask "In how many years was he alive", but "How many years was he alive", therefore asking for the age

[u/Ancient_Yellow_709 → u/Myclarinetto]

But they didn't tell us his birthday! They gave us his birth year and death year in the textbook, as mentioned.

There was no reasonable way for us to know how old he actually was (this was when Wikipedia wasn't trusted and looking stuff up in encyclopedias was onerous, since we'd be unlikely to have a book on this guy in our school library).

So my interpretation was at least as reasonable an interpretation. And I included the dates he was born and died. I clearly knew the material that was being tested. That teacher was a prick to give me zero points even if he disagreed with my math. He'd give other students who did zero work but who had rich parents or who worked for the school partial credit for getting stuff wrong without showing work.

[u/Myclarinetto → u/Ancient_Yellow_709]

I agree, the teacher was a prick because you wrote the years. When you don't know the exact dates you assume the birthday has already happened, for example 2000-2010: the person has 10 years

[u/TotientEC → u/ExamplePractical1981]

So what you're saying is you learned something important in 7th grade that you will never, ever forget.

[u/HarbingerML]

Just to clarify, you are saying you refuse to tell them what 63/90 is as a percent out of principle .. so your child is not capable of expressing this fraction as a percent but your main concern is they know the general probability of a coin flip (assuming the coin is a fair one - which incidentally is stated nowhere in the problem)

Maybe you should worry a little more about helping your son with more elementary skills and a little less about self-congratulatory gotcha moments.

[u/gibbylewd → u/HarbingerML]

Reminds me of that dude who refused to teach his (young) kid how to use a can opener when she was hungry so she could learn critical thinking skills, and he wrote a pseudo-intellectual essay on twitter about how deep and philosophical he is

[u/drbeerologist → u/gibbylewd]

Good ol Bean Dad

[u/Opus_723 → u/HarbingerML]

Kid understands this is just a lame prompt to get him to calculate a percentage and is trying desperately not to get a bad grade because his dad wants to look smart.

[u/miaomiaou → u/HarbingerML]

I mean, hopefully the child was taught how to calculate a percent from a fraction as a part of the lesson. Hopefully the child is able to actually do the calculation without their father simply telling them that percentage.

[u/LukeLJS123]

μ=0.7 and σ=0.04830, so x=0.5 has a z-score of -4.1408, so the p-value is 0.00001730, and with α=0.05, we can assume that this is not a fair coin

i took stats in 2023 so don't come for me if i should have assumed that the mean is 0.5 instead of 0.7, my point still stands that this is almost definitely not meant to be a fair coin

edit: i think we should assume the coin is fair and do the math based on that, since that is what we are assuming. the null hypothesis is that the coin is fair, so that should be our μ, 0.5

so when μ=0.5 and n=90, σ=0.05270, and with x=0.7, z=3.795, so P(z>3.795)=0.00007382, which still falls well below α=0.05, thus the coin is most likely unfair

[u/stateofsirens]

It may not be a 50% chance if the coin isn't noted to be fair. The probability of the next flip being heads is 50% only if there is actually a 50% chance of it happening on all flips. Just because the trial outcomes are not influenced by previous outcomes does not mean that it's automatically a 50% chance.

[u/Biochemicalcricket → u/stateofsirens]

Also, with sufficient sampling you can prove it isn't 50/50 but over 90 flips you're still WELL short of that proof, but one would be fair to assume over 2/3 is a major deviation from 50/50. It's improbable that the coin is balanced even at that without additional info as presented.  

Really shit question to try to prove a point on without reworking it

[u/Rattus375 → u/Biochemicalcricket]

1/10k odds for a fair coin to be that imbalanced after 90 flips

[u/ByeGuysSry → u/Rattus375]

1 in 5k. I think you mistakenly calculated the odds of getting heads at least 63 times, when you should instead calculate the odds of getting heads at least 63 times OR tails at least 63 times

[u/Xezron2000 → u/ByeGuysSry]

Damn, this guy fucks in math

[u/SportResident8067 → u/stateofsirens]

Teach them how to calculate a standard deviation and the real answer is 70% with an error bar.

[u/Happy-Plant458]

it should definitely be asking what percent of the results was heads but i feel thats an argument you should be having with the teacher not your kid

[u/RelativeThese2634 → u/Happy-Plant458]

How else am I going to get fake internet points tho!!!

[u/Captain-Griffen]

P value of 0.000188. Don't think that's a fair coin toss.

[u/Rikki-Tikki-Tavi-12 → u/Captain-Griffen]

This. If I have it right, the chance of this coin being fair is about 1 in 15k

[u/PissMissileTopTitty → u/Rikki-Tikki-Tavi-12]

So glad to see some sanity in this thread. Sure, it's a gr7 class, still very much worth pointing out that the information provided strongly suggests the coin is weighted

[u/ThePevster → u/Rikki-Tikki-Tavi-12]

Not quite right. A p-value of 0.000188 implies that, if the coin was fair, the chance of observing an outcome as or more extreme as this one is 1 in 15k. As or more extreme meaning either 63+ heads or 63+ tails out of 90 heads as the previous commenter did a two sided hypothesis.

In a frequentist framework (which is where p-values come from), the coin is either fair or not fair as a state of nature. We cannot assign a probability to the coin being fair.

[u/developer-mike → u/Captain-Griffen]

Yes, and in math courses you'll often see "fair coin" if you're supposed to assume 50%. This question does not say "fair coin."

[u/TheCunningRabbit]

As a math teacher with years of teaching this grade in experience, this needs clarification. Is the teacher requesting the theoretical probability or the experimental.

The theoretical probability is 1/2 or 50%. The experimental probability is 63/90 or 70%. Without knowing the type of probability that the teacher wants you can't be sure which answer the teacher wants.

[u/FashionableLabcoat → u/TheCunningRabbit]

Thank you. I remember arguing with my own gradeschool math teacher about this when I was in school— theoretical vs experimental probability needs to be specified!

[u/33rpm_neutron_star → u/TheCunningRabbit]

As a statistician, I have never heard anyone call this “theoretical” and “experimental” probability. You might estimate the probability based on data and/or some priors, and you may hypothesize a particular value, or consider a range of models to compare with differing values, but “probability” in this context is generally thought of as a population quantity (aka, always in some sense “theoretical”). 

[u/TheCunningRabbit → u/33rpm_neutron_star]

It's part of the standards as 7.sp.c.6.

While at the high school and beyond level you are extremely correct, at the middle school level it is helpful for students to break down probabilities this way. One such reason is understanding the gamblers fallacy. Another is for being able to discover when their calculation of "theoretical" probability is wrong. It may be best to think of it as a stepping stone towards a deeper understanding or a better understanding of how things work.

[u/WomanInTheWood]

That depends on if your child is named Rosencrantz or Guildenstern. If so, 100% heads.

[u/gailonmiles]

Fwiw we finished the homework writing 70%

[u/TankApprehensive3053 → u/gailonmiles]

Update when it gets graded.

[u/Suspicious_Board229 → u/gailonmiles]

worthwhile to remember that it's a 7th grade math question and not a reading comprehension or statistics test. 70% is likely the answer they wanted.

[u/Numerous_Photograph9 → u/Suspicious_Board229]

I recall math class spending time looking at what was relevant to the equation at hand. Reading comprehension was a big factor in understanding when it come to word problems.

[u/yaourted → u/Suspicious_Board229]

Math involves reading comprehension all the time. Huh

[u/gailonmiles]

A few clarifying points while we wait for the grading of the assignment tomorrow!

1) the homework was kind of a multi topic review. Other questions included fractions, event likelihood, number lines, frequency, a question about number of expected results by rolling two dice, and this question. The homework title is "warm up week of October 12" so no implication of what probability this question should be.

2) So obviously next step was look at what he was working on for the week and LITERALLY the first two worksheets behind this homework one is titled "theoretical probability" and the second is titled "experimental probability." I kid you not.

So I'm not sure any more of what answer the teacher is expecting but my original frustration is still focused on that this is an ambiguous and confusing question.

Update tomorrow promised!

[u/Comprehensive-Ease10 → u/gailonmiles]

Yeah, as a middle school math teacher myself, that's a terrible question LOL.

The probability (suggesting future) of it landing on heads-- or tails-- is of course 50% (I don't think we can reasonably assume that it's an uneven coin, especially with a relatively small sample size and unless it was explicitly stated).

However, the way the question is worded and based on the information given, in combination with the other things they are learning about, suggests that the teacher might be looking for the 63/90 as the fraction that demonstrates the previous results, even though that's not a probability in this case.

That's disheartening to see. Best of luck to your 7th grader. I would give them an A for discussing it with their parents and having what sounds like a lively math discussion about a very stupid problem.

Perhaps they could print out this thread and bring it in to back up their work 😜

[u/grundleHugs → u/Comprehensive-Ease10]

This question is to get the student to think about the hot hands fallacy of statistics. The previous result does not affect the outcome. It doesn't matter that the coin seems to come up heads more. The chance is still 50%

[u/MrInCog_ → u/Comprehensive-Ease10]

To be fair I’d still take some points off for not writing it in percent as the only unambiguous part of the task states, better yet not even in simplified form of 7/10.

[u/randomlurker124 → u/Comprehensive-Ease10]

If I flipped a coin 90 times and the results were that skewed, I would almost certainly and reasonably assume the coin is uneven. 90 flips is not a small sample size and more than sufficient to demonstrate statistical significance. This would absolutely pass phase 1 medical trials for example, if the question was whether a drug worked. 

[u/Any_Flan_6776 → u/gailonmiles]

They should write both answers as theoretical and experimental solutions

[u/redditydothis → u/gailonmiles]

Regression to the mean is a thing. 90 flips should be very close to 50/50. The coin must be altered or something.

[u/Ill_Disk_1115 → u/gailonmiles]

In statistics somethjng is considered statistically “significant” in a population or set if it occurs farther than about 2 standard deviations away from the mean (approx < 5% chance). The probability that a fair coin would land on any single side 63 times is 0.0094%. Said another way, 95% of all 90-flip experiments would result in a range of 36-54 heads… 63 is nowhere near this.

TL;DR Your son is right. The most correct answer is 63/90. There is only a 1 in 10,600 chance that this is a fair coin

[u/usersince2012 → u/gailonmiles]

In the meantime, just look at this discussion you prompted. Yikes!

[u/bren_derlin → u/gailonmiles]

Just write both answers. The theoretical probability is 50%, the experimental probability is 70%. It’s not like it’s multiple choice.

[u/kdizzle619]

This thread reveals how many people took statistics and its clear not many

[u/Sonamdrukpa → u/kdizzle619]

To be fair the first thing anyone who's taken statistics is going to say about this problem is that it's a badly written problem

[u/Sidoen → u/kdizzle619]

Look at the names, they're mostly GenAI bots I think.

And look at what they're saying, it's all worded to drive you nuts, make you comment to point out the flaws in their reasoning.

Dead internet right there!

[u/kdizzle619 → u/Sidoen]

I hope so, because it's sad to see so many confidently incorrect people

[u/Flat-Structure-7472]

As a teacher myself you need to work on your wording. "Write your answer as a PERCENT." is good. The other sentence should have been "What is the usual chance of a coin landing on either head or tails?".

[u/derpandderpette → u/Flat-Structure-7472]

Teacher hijacking the top comment to explain what is going on here. The students are learning about experimental vs theoretical probability. Theoretically it should be 50/100, but experimentally they got 63/90. I would bet dollars to doughnuts if we could see the rest of the worksheet it would say something about experimental probability somewhere on it.

Additionally, they are teaching how to convert fractions into decimals then into percentages. The students, likely using a calculator, are supposed to divide 63/90 to get 0.7. Then they are supposed to move the decimal place over two places to get 70%.

It’s actually annoying to see so many people here slamming the teacher and the problem when they have no idea this is a standard grade 4-6 outcome depending where you come from.

[u/Avocadonot]

Man reading these comments is dismal

[u/Beneficial-Band2604]

These questions are to help train people how to read and think critically. These were my favorite questions as a student because on homework where we shared our answers, I could see how many people simply didn't take time to read and understand the assignment.

It's a valuable skill, one that assists me to this day.

[u/Carbon-Base → u/Beneficial-Band2604]

Teaching kids critical thinking skills and common sense is immensely helpful and allows them to solve problems not just in math class, but in other classes and in life overall.

[u/Rokon_616161 → u/Beneficial-Band2604]

Now I read construction notes and point out not only the falsehoods in said notes, but also the short grammar or spelling or punctuation.

[u/ace-mathematician]

In probability, there are two calculation approaches: classical and empirical. The classical approach is based on the equally likely outcomes of H and T, and we calculate the theoretical probability as 1/2.

Empirical probabilities are based on the results of a performed probability experiment. In this case, the empirical probability of heads is 63/90.

Is this a poorly worded question? Maybe. Depending on the grade level, the students may not have been exposed to all the nuance yet.

[u/Accomplished_Ice5073]

Z Score = ([Actual number of heads] less [expected number of heads]) divided by the square root of ([Number of flips] divided by 4)

Z = (63 - 45) / sqrt(90/4) = 3.79

In order for the coin to produce 63 heads on 90 flips, it would have to fall outside of 3.79 standard deviations from the norm. This translates in a z-score table to a probability of 0.0075%. This is about a 1 in 13,333 phenomenon.

So there is approximately a 1 in 13,333 chance the correct answer is 50%, the coin was perfectly balanced and it just happened to land on heads that many times, and approximately a 13,332 in 13,333 the coin in not balanced and therefore our only information of the coin's bias is the 90 flip sample, therefore the best answer is 70% (63/90).

[u/33rpm_neutron_star → u/Accomplished_Ice5073]

A P VALUE IS NOT THE PROBABILITY THAT THE NULL IS TRUE

cough Sorry, just had to get that off my chest. Your claim about the chances of it being fair is incorrect and misworded. Overall I agree with your take though.

Also, the problem should ask for your “estimate” of the probability of heads (they’re not learning about hypothesis testing).

[u/beene282 → u/Accomplished_Ice5073]

The fact that something happening by chance is 1 in 13,333 doesn’t mean there is a 13,332 in 13,333 chance it happened by design GIVEN it has happened.

The chance of me winning the lottery is 1 in 10 million, but if I show up tomorrow with a fortune, you can’t say there’s only a 1 in 10 million chance I won the lottery therefore there is a 9,999,999 in 10 million chance I got the money some other way.

[u/ElethiomelZakalwe → u/Accomplished_Ice5073]

Computing the z score and finding the probability that it was a fair coin is well beyond seventh grade math. I would have thought they just made the implicit assumption that it was a fair coin and wanted the students to get that the odds of the next roll is independent of previous results.

[u/highgo1]

The question could benefit from having, "using these numbers" or something. Also, by 7th grade, studs should be able to reduce this fraction to 7/10. And then answer 70% for heads.

[u/Administrative_Bed5]

It doesn't say what kind of coin. If the teacher gave proper direction for the question, which is seems like they did based on the child's reaction, then you are causing problems by not allowing them to answer it properly.

[u/Djolumn]

When similar questions are asked in statistics classes they often refer to the coin as a "fair coin".

[u/Opus_723]

Good lord, all these pedants busting out college-level stats theory to argue with the specific wording of a middle school math problem.

The kid is smarter than all of you because he recognizes that this is just a vapid prompt to get him to turn 63/90 into a percentage.

[u/Dangerous_Seaweed601]

It didn't say flipped a fair coin, either, though.. so..

[u/swooptheowl22]

As someone with a bachelor's degree in statistics, this is such a bad question. They aren't learning about the law of large numbers in 7th grade (assuming this is a fair coin which isn't even mentioned).

We really need to raise the standards for teachers. I once got told I was doing algebra wrong in 5th grade and my parents had to get involved (both have PhDs in science).

[u/Knightrealmic → u/swooptheowl22]

I remember in fifth grade we were learning about calculating area based on more complex aggregate shapes. I asked about any arbitrary shape if we can approximate it by taking tons of smaller and smaller squares and she said that doesn’t work lol, it won’t ever get the right answer. That was something like twenty years ago

[u/KittyInspector3217 → u/Knightrealmic]

That confirms it, the moon landing was definitely fake. I knew calculus was bullshit!

[u/LackWooden392 → u/swooptheowl22]

Idk bro they taught me the law of large numbers in 7rh grade. They didnt call it that until 9th grade, but they did teach us that more iterations = more certainty

[u/TugleyWoodGalumpher → u/swooptheowl22]

We need to raise pay for teachers so people have a reason to meet the standards of being a teacher.

[u/LorenzoDePantalones → u/swooptheowl22]

Maybe they're sneaking in questions about maximum likelihood estimates of binomial distribution parameters to find genius 7th graders. Or fussy Dads.

[u/FormalWare]

Your seventh grader is a clever Bayesian.

[u/Integer_Domain]

I tutored a lot of primary ed majors in college. I would not want most of them teaching my child math.

[u/Separate-Pickle9963]

Experimentally, 63 heads out of 90 trials is a small amount of evidentiary reason to suspect an unfair coin. If we assume the coin is fair as a given, the answer is 50%. If you flipped the coin 100,000 times, 63/90 would level out unless it was unfair, since it can take quite a while for stochastic data to level out.

[u/TatterhoodsGoat]

What is stopping him from calculating 63/90 as a percentage on his own? Does he not know what percentage means, not understand fractions, not know how to do division, or not understand how decimal places work? All of those seem important for carrying on with understanding probability.

[u/rexjoropo]

The probability of flipping heads is/was always 50% and it always will be.

The fact that 63 of the 90 last flips were actually tails is irrelevant .

[u/Mrkvitko → u/rexjoropo]

Probability of *fair* coin toss are 50%.

[u/Competitive-Outside8 → u/rexjoropo]

With that distribution after 90 flips, I'd be starting to seriously question the fairness of that coin.

[u/MoultingRoach → u/Competitive-Outside8]

Of the flipper.

[u/djambates75 → u/rexjoropo]

It says nowhere that its a standard coin.

[u/Polyforti → u/djambates75]

This is for middle school mind you

[u/Neat-Second9923 → u/djambates75]

Middle school statistical analysis of odds that a normal coin would do 63/90 heads vs finding a weighted coin in the wild lol

[u/Raaxis]

The question is ambiguous.

“What is the probability of the next flip landing on heads?” cuts to the idea that probability in this case is independent of past results.

“What is the percentage of flips that were heads?” instead asks for interpretation of said past results.

That said, you’re being a bit pedantic for seventh grade math. It’s pretty clearly asking for a percentage. Explain that sometimes, word problems are written poorly and in those cases, you just choose the most likely intention/interpretation and move forward.

[u/prank_mark → u/Raaxis]

Kids in 7th grade are old enough to understand the concept of gamblers fallacy. I'm more surprised they're only learning percentages in 7th grade.

[u/roxgib_ → u/prank_mark]

Are they just learning percentages? It sounds like they are learning about probability and it happens to involve percentages

[u/TiltedLibra]

You know what the worksheet is asking, and by not helping your kid with the answer, the only person you are screwing is him.

[u/beastmaster11]

This isnt a poorly worded question. It is intentionally a trick question. Now maybe your kids teacher explained that but just wanted it to be a division question and youre just not listening to your kid. Or maybe your kid misunderstood. Either way, this isnt the hill to die on

[u/Aggressive_Grade_732]

Okay, so this is kind of the meme curve where there's two jedi and one angry person in the middle.

Bottom: It's 63/90

Middle: NOOO IT'S A FAIR COIN SO IT'S ALWAYS 50%!

Top: Statistically speaking, if we do a binomial test, then given 90 flips, and 63 successes, the chance of getting 63 successes or greater is 0.0001. As a result, we can determine that undrr a p-value of 0.05, the coin is not, in fact, a fair coin, so the best estimate we have of the probability of flipping heads is the current mean, i.e. 63/90.

[u/jwlgdgggm]

Though the question phrasing is problematic, the 50% rule applies only to a fair coin. In fact given the fact that you are landing a 63 vs 27, from either frequentist or Bayesian point of view, the best estimation for the probably will not be 50%.

[u/Random_Guy_47]

The question isn't poorly worded.

It's testing if you understand that the result of the next flip is unaffected by the results of the previous flips.

The coin also isn't uneven. Flip it enough times and it's entirely possible that in 90 consecutive flips you get 63 heads and 27 tails.

[u/BODYBUTCHER → u/Random_Guy_47]

theres no reason to assume its a fair coin

[u/MomLovesMeBest → u/Random_Guy_47]

It is indeed poorly worded. The question doesn't specifically ask about the next flip, you are assuming that's what it's asking, which is inherently what makes it poorly worded.

[u/Random_Guy_47 → u/MomLovesMeBest]

You're not wrong but that is implied.

That feels like something so obvious it doesn't need to be specified.

[u/CivilizedPsycho]

The comments in this thread are r/mildlyinfuriating as are you OP.

Yes, literally speaking the probability of landing on heads is 50%, but in no world is a 7th grade math class asking for the literal odds of a coin flip. It's not a riddle, and it's not meant to be a trick question. It would also never be implying that it's a nonstandard coin and that the flipper is trying to figure that out. Y'all are WAY overthinking it.

With ANY level of critical thinking y'all would realize that it's a poorly written question and that the 7th grade math teacher is definitely looking for the percentage of times it landed on heads. 63/90 translates to 7/10, or 70%.

If the teacher marks 70% as wrong, come back and tell me please because in that case, the teacher is TA.

Editing to add: We also have the information outside of the paper to work with. The kid told their parent "it's not how the teacher taught us." The teacher wants the total percentage of thrown heads but completely botched the question. You are right that the literal answer as written is 50% but it's not what the teacher is looking for. It was written wrong based on what they're clearly being taught. If the kid writes 50%, next week we're gonna see a r/mildlyinfuriating post that they got it wrong with folks flipping out about the teacher anyway, just like the stupid equation you see posted every week.

[u/Reasonable_Gas9555 → u/CivilizedPsycho]

I teach grade 6 math and I had a question similar to this one on my test. However, I did explicitly teach that just because a coin/dice/whatever happens a certain amount of times in a row, doesn't change the statistical probability of something happening. I also tell them to be aware that there will be a question like this on a test and we do many examples.

[u/anotherlebowski → u/Reasonable_Gas9555]

This is why I don't like the comment "It's not a riddle", which I've seen multiple times on posts like this.  Logic matters.

The probability is 0.5.  That's not semantics.  That's how it works.

Also, this is 7th grade which makes this way worse.  First grade I would still argue this is incorrect but forgiveable.  7th is ridiculous.

[u/Outside-Dress594 → u/Reasonable_Gas9555]

Ya. This question is posed to make this specific point

[u/yaourted → u/CivilizedPsycho]

It directly asks “what is the probability of landing on heads?”. It doesn’t ask what percentage of the time that it did. You can’t just say it’s “poorly worded” when it’s a whole different concept.

[u/blandarflek → u/CivilizedPsycho]

So shit like this is why school was traumatic as an autistic kid.

The question asks the probability of heads. If you want a different answer then word it correctly.

[u/Alita-Gunnm → u/blandarflek]

Exactly this. It shouldn't be the kid's responsibility to figure out what the writer intended to ask, simply to answer what WAS asked.

[u/topturo77 → u/CivilizedPsycho]

I learned basic probability in 7th grade. One of the defining principles of probability is that previous results do not affect future tries. This is literally a question I got in 7th grade and the answer is and always will be 50%, unless the question specifically states the coin is unfair. This is, in fact, one of the CLASSIC trick questions when introducing the concept of probability, precisely because humans natural inclination is to answer what you did, which is wrong. 

[u/cyanraichu → u/topturo77]

It's not even a trick question. If you were explicitly taught this basic principle of probability it's literally just checking to see if you retained that extremely relevant information

[u/mr_f4hrenh3it → u/CivilizedPsycho]

It’s a bad question. If the answer can at all be debated or needs to be seen through the lens of a 7th grader to understand, then it’s obviously a bad question. That’s what most people here are saying

[u/cyanraichu → u/CivilizedPsycho]

couldn't disagree more. When we learned about probability in school we learned that the probability of a coin flip was always 50%, even if the coin had come up heads three times in a row before or whatever. One of the basic principles of probability is it doesn't change because of a prior outcome.

If the question wanted to know the percentage of time the coin had already landed on heads, it should have asked that. Assuming a child would know the question actually meant something different than what it was asking seems a lot more riddle-ish to me than assuming a 7th grader would understand basic probability about things like coin flips and die rolls

[u/MrDSkis94 → u/cyanraichu]

I feel like that is the entire point of telling you how many times it landed on each. It is deliberate to try and get you to give the percentage instead of the probability specifically to illustrate that the outcome of the actual coin flips doesn’t change the probability of the coin flip itself. I had many math questions like this in high school that were designed to mislead you to see if you would still come to the correct answer through critical thinking.

[u/cyanraichu → u/MrDSkis94]

I agree but I don't even think it's being intentionally misleading. It's designed to ask if you understand one of the very first things you're taught about probability

[u/Kagahami → u/cyanraichu]

I've seen a whole wealth of trick questions written in exactly this manner that encourages students to read carefully and not assume an answer based on the information given.

Either it's a trick question where the answer is 50%, or the question is written poorly. I think it might very well be the former.

[u/Adept-Caterpillar-31 → u/cyanraichu]

Bayes has entered the chat.

[u/The-Yar → u/cyanraichu]

Exactly. I might agree with the comment above yours if it weren't for the fact that this is a very common question and answer when studying probability. Previous flips have no impact on a flip, and this is an important and fundamental concept in probability. If the answer isn't 50% then this question is literally pushing the same kind of crap that people are pushing when they sell phony strategy books on how to beat roulette.

[u/ThisIsMyGeekAvatar → u/cyanraichu]

You’re right. Anyone defending this question is straight up wrong. Words have meaning - especially in math. 

If the test didn’t want the answer to be 50%, they shouldn’t have used the word “probability”. This isn’t just simplifying a problem, it’s literally making a false statement. 

[u/Powered-Lamb → u/CivilizedPsycho]

in no world is a 7th grade math class asking for the literal odds of a coin flip.

In a world where the lesson just got done discussing dependent and independent probability, yes, a 7th grade math class might ask for the literal odds of a coin flip. The rest of the information is there to be irrelevant by design.

[u/Playful-Visit4761 → u/CivilizedPsycho]

Clearly you did not participate in 7th grade math. This type of question has appeared across multiple grades, 7th included.

[u/Sadboi395]

Wouldnt it just be 50% bc the previous results have no bearing on the next flip? Just awfully worded question

[u/hikerguy555]

The more than mildly infuriating part is everyone's validation of OPs outrage here. I guess it speaks to how traumatic middle school math was for many of us, that getting angrily defensive and starting a whole absurd side thing instead of admitting you don't know how to do the math is what we should be modelling for our kiddos?

[u/Shouldacouldawoulda7]

It's not poorly worded - it's a critical thinking question.

It's specifically referencing the gambler's fallacy, wherein one believes that the past outcomes of a random chance event will have an impact on the future probability of the same random chance event. I.e, "I flipped a coin 10 times and it came up tails 10 times, which means the next flip has to be heads."

[u/rs1971 → u/Shouldacouldawoulda7]

It is poorly worded. If the intent is to test understanding of the gambler's fallacy (and it probably is), it should say 'what is the probability of landing on heads ON THE NEXT FLIP'. As stated, it's a bit ambiguous.

[u/godfromabove256 → u/Shouldacouldawoulda7]

Huh, I thought it was targeting the hot hand fallacy, which is just the opposite. Good thing it's smack dab in the middle of the two.

[u/OkMidnight8144]

It bothers me how this is a trick question to teach critical thinking is even being debated. The answer is 50%, it's to teach kids how to identify and disregard irrelevant information to signify that they know how percentages actually work. If a 7th grader doesn't know a coin only has 2 sides that is a very big problem.

[u/scipionerva → u/OkMidnight8144]

A correctly written question will ALWAYS say "Sophia flipped a FAIR coin", given that the coin cannot be assumed to be fair based on how the problem is written the correct answer is that it's impossible to tell what the true possiblity is from the question and sample data.

Back when I was a grader I would probably give 50% at least half credit, but it's not correct as the problem is written.

[u/Veyron2000 → u/scipionerva]

If it said “flipped a fair coin” the answer would be 50%, but if they were looking for an answer of 70% (a biased coin) they obviously shouldn’t say the coin was fair. 

[u/tumbled_leather]

Your 7th grader is demonstrating that they have learned how to play the game AND preserving their grades by doing it how they learned in class from the instructor

Why not show your 7th grader how to calculate both and stop being a juvenile

[u/Neat-Razzmatazz-5837]

63/90 is the best estimate but not the true value. The problem doesn’t specify if the coin is fair or not, the parent OP here is bringing in that information by assuming all coins are fair. It could be better worded, but that is how I understood it and I do stats. 

Also, a lot of people don’t know statistics at all and just assume that in any case if they count two possibilities it is a “50 50 chance”. That is just bad thinking. Now if the problem specified that it was known to be a fair coin or if the problem was asking if there was enough data to conclude that the coin was unfair now we’re asking more statistical questions. 

[u/elangomatt]

It is definitely a bad question. Based on the first part of the question I assuming they are expecting a 70% answer. If they wanted to be tricky then the question could have been "What is the probability of landing on HEADS on the next flip?" or better yet "What is the probability of landing on HEADS on the next flip of a fair coin?". In that case, then 50% would have been correct and nobody gives a fuck about Sonia. The probability could only be 70% if the coin wasn't a fair coin.

The question should have been phrased as "What percentage of coin flips landed on HEADS?" if they want 70% as the answer. It shouldn't be using the word probability because Sofia's flips has nothing to do with future flips of the coin.

[u/freegerator]

It doesn’t call it a fair coin

[u/TheeDragon]

It's pretty obvious what the teacher is asking for, idk why you feel the need to be a jackass to your son over something so simple.

[u/Rokon_616161 → u/TheeDragon]

Probability means next flip, not previous flips. History has no bearing on future probability.

[u/twelve34am → u/TheeDragon]

I’m surprised people think that 7th graders never get trick homework questions, especially in a math class. You can take algebra in 8th grade and geometry in 9th. I think it’s asking the students to think critically. They undoubtedly learned about coin flipping within the first 30 seconds of learning statistics.

So I say it is meant to be ‘50%’.

In 7th grade I would have put 63/70 and so would have the rest of the class. And the teacher would mark all of our papers and complain that we were the worst batch of students to have ever come through her class and we never listen. I don’t miss middle school lol

[u/LichenTheMood]

The information provided suggests that this coin is not fair. However there is still a small statistical chance that it could be fair.

The question cannot be answered. There is insufficient information to determine if it’s a crooked coin or not. And if it is a crooked coin what probability is associated with it.

Yes. I struggled a lot in school.

Yes it is autism.

[u/dcgrey]

Is there an expectation that there is a correct answer, or is this a question to interrogate thought processes? I’ve loved some of the seventh grade questions I’ve seen where the debate we’re having here is what gets argued about in the classroom. Everyone shows their process of coming up with different answers. Sure beats asking four very specifically worded variations on one question.

[u/MoogleyWoogley]

Probably is still 50%. If they wanted 63/90 the the question should be about the percentage of the heads outcomes in the 90 flips test.

[u/throwed101]

70% it doesn’t say if you flip the coin again. In this context it is asking what was the probability of the results.
I could see the wording being confusing,

[u/stupidfock]

If I’m betting on heads then the odds of heads is usually 0%

[u/Easy_Lengthiness7179]

Probability of the next flip, vs the calculated probability of the previously flipped coins.

[u/optimisticanthracite]

I agree that the question is worded poorly but I’m assuming they meant “what is the EXPERIMENTAL probability of landing on heads?” in which case the 63/90 would be the right answer.

Editing to add that the very clear solution to this is to have your kid ask the teacher about it tomorrow at school.

[u/realbobenray]

"Sofia flipped a coin 1 time and it landed on heads 1 time and tails 0 times. What is the probability of landing on HEADS?"

[u/bob-loblaw-esq]

This seems like the online casinos are running our math classes.

[u/Dock_Ellis45]

This teacher needs to learn about the Law of Large Numbers.

Also, for those wondering, the expected answer is 70%.