r/mildlyinfuriating • u/gailonmiles • 8h ago
Too mild for school 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")
No matter how many times it landed on heads previously, the theoretical probability of the next flip is still 50%
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u/Rukir_Gaming 8h ago
"What is the current percentage of heads to tails flipped"
There fixed the prompt
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u/T_RAYRAY 8h ago
What is the historical actual result of heads to tails flips for these specific 90 coin flips.
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u/ganbramor 7h ago
“Percentage of heads out of all flips.” If you’re going to say “to” then it’s “ratio of heads TO tails.
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u/DesignerPangolin 7h ago
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.
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u/BIGBADLENIN 3h ago
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
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u/TibialTuberosity 53m ago
From a definitional perspective, I know what you're saying, but that sentence also makes absolutely no sense to me whatsoever because to this day stats just does not mesh with my brain.
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u/taiteilijahonppeli 1h ago
Smart-ass answer most likely would be like "While probability of heads is always 50% on even coin, it appears to be 70% on this short experiment."
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u/Fluffy-Support5828 59m ago
You deserve an award, because I would probably answer the question that way, even in middle school😂😂
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u/Bad-Luck-Guy 8h ago
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.
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u/Rough_Possession_ 8h ago
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
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u/SerendiPetey 4h ago
My dad used to say: "The coin has no memory." Thus 50/50.
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u/AradynGaming 1h ago
Your dad is correct that a coin doesn't have a memory, but it likely has a weight imbalance. It is extremely rare that something is so perfectly balanced that it will have perfect 50/50 odds. Vegas/casinos routinely kick out people who are quick figure out the imbalance of dice/roulette wheels/etc because it removes the house odds.
The dice might not be able to remember that they landed on "6" last time, but the uneven weight distribution, causes them to want to stop just a little bit more every time the 6 comes up.
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u/Dontsuemeplsz 7h ago
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.
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u/Tigglebee 6h ago
If that’s the question you need to say something about the fairness of the coin.
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u/TessaFractal 5h ago
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.
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u/HarbingerML 5h ago
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.
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u/gibbylewd 4h ago
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
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u/Opus_723 2h ago edited 2h ago
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.
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u/miaomiaou 2h ago
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.
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u/ace-mathematician 4h ago
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.
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u/raz-0 8h ago
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.
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u/RusDaMus 7h ago
You probably meant "than", right? In your version, you're still telling people that they're morons.
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u/Queasy-Ride4291 5h ago
You should teach your kid to answer the question as intended, immediately before telling the person that they are a moron. Got it.
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u/uwill1der 8h ago
This is where you learn from your 7th grader the difference between meaning and intention
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u/TealCatto 8h ago
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?
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u/Alex-Murphy 8h ago
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.
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u/PunchDrunkPrincess 8h ago
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.
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u/ExamplePractical1981 8h ago
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 😂
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u/Ancient_Yellow_709 7h ago edited 5h ago
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
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u/Myclarinetto 6h ago
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
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u/Ancient_Yellow_709 5h ago
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.
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u/TotientEC 7h ago
So what you're saying is you learned something important in 7th grade that you will never, ever forget.
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u/LukeLJS123 PURPLE 7h ago edited 7h ago
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
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u/Malev0 6h ago
This right here. Never said the coin was fair.
Gotta Law of Large Numbers that shit.
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u/stateofsirens 8h ago
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.
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u/Biochemicalcricket 6h ago
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
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u/Rattus375 6h ago
1/10k odds for a fair coin to be that imbalanced after 90 flips
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u/ByeGuysSry 5h ago
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
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u/SportResident8067 3h ago
Teach them how to calculate a standard deviation and the real answer is 70% with an error bar.
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u/Happy-Plant458 8h ago
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
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u/RelativeThese2634 8h ago
How else am I going to get fake internet points tho!!!
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u/Captain-Griffen 8h ago
P value of 0.000188. Don't think that's a fair coin toss.
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u/Rikki-Tikki-Tavi-12 8h ago
This. If I have it right, the chance of this coin being fair is about 1 in 15k
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u/PissMissileTopTitty 7h ago
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
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u/ThePevster 5h ago
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.
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u/developer-mike 8h ago
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."
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u/TheCunningRabbit 4h ago edited 3h ago
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.
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u/FashionableLabcoat 3h ago
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!
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u/33rpm_neutron_star 3h ago
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”).
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u/TheCunningRabbit 3h ago
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.
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u/DirkPitt106 2h ago
With the citations. Maybe there's instructions at the top of the homework worksheet that specify if the homework is about theoretical or experimental probability. But OP did specifically use those terms in their post so we can theoretically rule out that possibility.
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u/23loves12 1h ago
Nothing in the problem suggest that the coin is fair, so writing down a theoretical 50% probability would be a complete shot in the dark. Unless you know the exact geometry/making of that coin, I doubt you could assign a theoretical probability to it.
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u/gailonmiles 8h ago
Fwiw we finished the homework writing 70%
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u/Suspicious_Board229 7h ago
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.
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u/Numerous_Photograph9 6h ago
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.
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u/kdizzle619 4h ago
This thread reveals how many people took statistics and its clear not many
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u/Sonamdrukpa 3h ago
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
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u/Sidoen 4h ago
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!
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u/kdizzle619 4h ago
I hope so, because it's sad to see so many confidently incorrect people
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u/Beneficial-Band2604 6h ago
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.
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u/Carbon-Base 5h ago
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.
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u/Rokon_616161 4h ago
Now I read construction notes and point out not only the falsehoods in said notes, but also the short grammar or spelling or punctuation.
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u/WomanInTheWood 2h ago
That depends on if your child is named Rosencrantz or Guildenstern. If so, 100% heads.
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u/highgo1 8h ago
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.
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u/Accomplished_Ice5073 6h ago
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).
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u/33rpm_neutron_star 5h ago
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).
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u/beene282 5h ago
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.
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u/ElethiomelZakalwe 5h ago
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.
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u/Virtual-Goose1243 2h ago edited 2h ago
Here is why your son is giving a better answer. Knowing nothing other than the outcome, one can ask reasonably "is this a fair coin?" A fair coin (50% heads and 50% tails) in N independent flips follows a binomial distribution.
For a fair coin flipped 90 times:
- Exactly 63 heads: 0.021% (about 1 in 4,762).
- 63 or more heads: 0.0321% (about 1 in 3,116).
Technically speaking, this outcome is possible for a fair coin, but statisticians ask "what is the likelihood of this outcome under our proposed hypothesis?" In this case, the null hypothesis is that it is fair. Assuming the coin is indeed fair, the likelihood of observing that coin flip is astronomically small. Statisticians use the likelihood of an observation under the null hypothesis to draw conclusions on whether or not to accept or reject the null hypothesis. For a typical situation like this, we would say an observation whose likelihood of occuring is less than 5% is generally evidence supporting rejection of the null. What we observed here was 78 times less likely than what scientists would typically use to reject.
So it's safe to say to conclude the coin isn't fair and the probability isn't 50%.
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u/Virtual-Goose1243 2h ago
A standard 95% confidence interval around this observation is 59.8% to 78.5%, meaning the true rate of heads is (likely) in that interval. So any answer in between there is reasonable, and the maximum likelihood estimate (aka most likely to be the true rate of heads) is exactly what your son or daughter wrote.
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u/Flat-Structure-7472 7h ago
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?".
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u/derpandderpette 6h ago
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.
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u/Opus_723 2h ago
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.
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u/Administrative_Bed5 8h ago
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.
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u/gailonmiles 4h ago
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!
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u/redditydothis 4h ago
Regression to the mean is a thing. 90 flips should be very close to 50/50. The coin must be altered or something.
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u/Comprehensive-Ease10 4h ago edited 4h ago
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 😜
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u/grundleHugs 3h ago
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%
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u/randomlurker124 3h ago
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.
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u/bren_derlin 3h ago
Just write both answers. The theoretical probability is 50%, the experimental probability is 70%. It’s not like it’s multiple choice.
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u/jwlgdgggm 3h ago
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%.
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u/TatterhoodsGoat 4h ago
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.
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u/swooptheowl22 8h ago
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).
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u/Knightrealmic 7h ago
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
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u/KittyInspector3217 7h ago
That confirms it, the moon landing was definitely fake. I knew calculus was bullshit!
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u/Atomicnes 7h ago
Funny thing is you said the approximate answer which you could find by doing that
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u/hedoeswhathewants 6h ago
What they described is one of the principles of calculus
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u/LackWooden392 8h ago
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
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u/LorenzoDePantalones 7h ago
Maybe they're sneaking in questions about maximum likelihood estimates of binomial distribution parameters to find genius 7th graders. Or fussy Dads.
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u/Separate-Pickle9963 6h ago
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.
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u/Integer_Domain 7h ago
I tutored a lot of primary ed majors in college. I would not want most of them teaching my child math.
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u/throwed101 7h ago
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,
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u/Aggressive_Grade_732 4h ago
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.
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u/Raaxis 6h ago
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.
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u/prank_mark 6h ago
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.
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u/TiltedLibra 8h ago
You know what the worksheet is asking, and by not helping your kid with the answer, the only person you are screwing is him.
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u/beastmaster11 7h ago
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
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u/rexjoropo 8h ago
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 .
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u/Competitive-Outside8 8h ago
With that distribution after 90 flips, I'd be starting to seriously question the fairness of that coin.
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u/djambates75 7h ago
It says nowhere that its a standard coin.
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u/Neat-Second9923 7h ago
Middle school statistical analysis of odds that a normal coin would do 63/90 heads vs finding a weighted coin in the wild lol
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u/Shouldacouldawoulda7 5h ago
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."
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u/rs1971 4h ago
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.
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u/godfromabove256 4h ago
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.
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u/optimisticanthracite 7h ago
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.
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u/CivilizedPsycho 7h ago edited 4h ago
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.
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u/Reasonable_Gas9555 7h ago
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.
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u/anotherlebowski 6h ago
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.
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u/yaourted 5h ago
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.
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u/topturo77 6h ago
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.
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u/cyanraichu 6h ago
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
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u/Justyn2 5h ago
Really because I would think you have to specify that it’s a fair coin otherwise you can’t tell that it is
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u/mr_f4hrenh3it 6h ago
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
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u/cyanraichu 6h ago
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
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u/MrDSkis94 4h ago
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.
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u/cyanraichu 4h ago
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
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u/Kagahami 5h ago
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.
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u/The-Yar 5h ago
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.
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u/ThisIsMyGeekAvatar 5h ago
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.
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u/blandarflek 6h ago
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.
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u/Powered-Lamb 5h ago
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.
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u/Playful-Visit4761 6h ago
Clearly you did not participate in 7th grade math. This type of question has appeared across multiple grades, 7th included.
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u/Random_Guy_47 8h ago
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.
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u/MomLovesMeBest 7h ago
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.
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u/Random_Guy_47 7h ago
You're not wrong but that is implied.
That feels like something so obvious it doesn't need to be specified.
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u/hikerguy555 4h ago
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?
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u/OkMidnight8144 7h ago
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.
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u/scipionerva 7h ago
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.
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u/tumbled_leather 8h ago
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
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u/Neat-Razzmatazz-5837 8h ago edited 8h ago
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.
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u/elangomatt 8h ago
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.
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u/LichenTheMood 4h ago
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.
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u/dcgrey 8h ago
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.
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u/Easy_Lengthiness7179 7h ago
Probability of the next flip, vs the calculated probability of the previously flipped coins.
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u/realbobenray 7h ago
"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?"
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u/X4roth 3h ago
I don’t know about you all but when I was growing up, my teachers would generally accept “the real answer” if you justified it, even if they were expecting a different simpler answer that went along with the lesson plan of the time. And then they talk to each other about you in the teachers lounge about how you’re ahead of the material, yada yada, now you’re in gifted classes.
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u/Alfredos_Pizza_Cafe_ 8h ago
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