At my job we have a football pool with mandatory participation. My first year working this job, half out of protest and half as a joke, I decided to choose my teams using a 20 sided die (because I’m a dnd nerd, not a football nerd). The rules of this football pool are this:

1. Each week you are to choose one team. You get one point if that team wins, and zero points if that team loses.

2. You can only choose each team once, until the play offs. (For example if you pick the chiefs week one, you can’t pick them again.)

3. Once it’s the playoffs, you pick one winner per game, and get one point per victory. Repeat each week leading up to the Super Bowl, where you again pick one team to win, and get one point if you do.

4. Whoever has the most points at the end wins.

Here’s where the disagreement lies:

I said there’s a 50% chance each week I pick a winning team. People who know more about football than me say I don’t, and that my logic is flawed. Three years of debating every football season the same arguments over and over again, and each side remains unconvinced of the other’s opinion. I’ll be honest here and say I’m a very argumentative person who loves math, so I’ve been completely unable to let this go. No one cares about this anywhere near as much as I do.

My argument is this:

I pick a random number between 1 and 20 by rolling a 20 sided die, then pull up that week’s football schedule, and count down from the top. (For example if the first scheduled game is dolphins vs jets, and I roll a 2, I am picking jets.) If I roll a team I’ve already picked, I just reroll until I get a new team. Basically I am rolling a die to randomly pick one out of 20 teams, playing against each other in 10 different games. Half of those teams will win, and half of them will lose, which means I have a 10/20 chance of picking a team that wins. In other terms, 50%. (For the playoffs I just flip a coin for each game, which everyone agrees is a coin flip, literally, for scoring a point.)

Here are the main counter arguments:

1. Each individual team does not have an equal chance of winning each week, because the teams are not equal. Team X could be favored to beat team Y for example, and therefore you do not have a 50% chance of winning if you choose team X.

2. Because you can’t pick the same team twice, you’re not picking between 20 teams every week. If hypothetically it’s week 6, I’ve already picked 5 teams, and I have 15 out of the 20 I’m rolling for left, 10 of those teams could win and 5 could lose, meaning I’d have ⅔ chance winning. Or the opposite. Or some other combination. The point being, as the season progresses, my chances change.

3. I’m only picking a number between 1 and 20, because I’m using a twenty sided die. That means there’s additional teams, scheduled at the end of the week, that it’s always impossible for me to pick.

4. What if there’s a tie? It’s not a binary outcome, because if two teams play against each other, there are 3 possible outcomes, not 2.

5. At the end of my first season doing this I had far more wins than losses, so surely, the odds cannot be 50/50 per week. (This one I have to believe is rage bait.)

And here are my counters to those counter arguments:

1. Let’s say for a hypothetical, team X is incredible, and team Y is atrocious. Sports analysts predict a 99% chance team X wins, and a 1% chance team Y wins. Would I still have a 50% chance picking a winning team between those two options? The answer, in my opinion, is obvious: Yes. Because I’m randomly choosing between them. I have a 50% chance picking a team that has a 99% chance of winning, and a 50% chance picking a team that has a 1% chance of winning. The odds of a team individually is irrelevant because the die does not know or care about these odds, and will not favor one or the other in its choice.

2. This I would agree this is in part true. However overall I still think I should in theory have a 50% success rate overall. Let’s say hypothetically, I pick at random 5 excellent teams weeks 1-5, and then I have 5 terrible teams left to pick from weeks 6-10. I’d have more chance of winning in the beginning half, and less chance of winning the second half. But following the logic I just used with point A, I should still come out with roughly equal wins and losses. If you, by week 10, can say “Because you’ve used up these 10 teams, and the remaining teams have different odds of winning,” and have some method of calculating each individual week given that information, I’d still argue it’s entirely random because the teams I picked at the beginning were random. I think it would be the same odds if I picked every team out of a hat week one, and went by that random selection list for the entire season. I don’t think choosing a random team each week changes the odds compared to choosing every week at random at once, even if week to week given the teams I have left you could theoretically predict different odds using outside information.

3. I could theoretically pick only the first game and flip a coin, I’d still have a 50% chance of picking a winning team. Out of 20 teams and 10 games, I have a 50% chance of picking a winning team, even if there are other games going on outside of them. Those other games are completely irrelevant to my odds of winning the ones I’m considering.

4. Ties are so rare I didn’t know they could happen until I had to pay attention to this stupid football pool. We had to write a new rule a couple years ago that a tie is half a point. It’s also theoretically possible for a coin to land on its side when you flip it, but we still call heads or tails 50/50. I think it’s reasonable to ignore it for that reason.

5. The second year I did this I had far more losses than wins. If you flip a coin 20 times and get tails 15 times, that doesn’t change the odds of the coin flip. There’s not enough data to use my results as evidence my math is wrong, that’s not how statistics works. The fact that year one I went into the Super Bowl tied for first place just means my coworkers are horrendous at picking good football teams.

I’ve asked several people for their input on this problem and every answer I’ve received has fallen into one of 3 categories. 1, a person who doesn’t like football but does like math and agrees with me, 2, a person who doesn’t like math but does like football, and overthinks it to death trying to explain why quarterback injuries or whatever change the odds, or 3, a person who doesn’t like football OR math, and wants me to stop talking to them. Therefore we involve the internet. Is there a flaw in my logic? And if there isn’t, is there a better way to explain my math to them? Is there something I’m missing here?

I put “f(0) could be any real number, since f is continuous and not strictly decreasing. For example, f(0) could be 0, or f(0) = 999999.”

I sketched two graphs both showing continuous functions hitting the two required points of (-1, 10) and (1, -20) with one going up to (0, 999999) in the center and the other passing through (0, 0). Graphs weren’t to scale but that doesn’t matter.

I got marked wrong for my answer of f(0) = 999999. My professor left the note “but you don’t know that.”

I brought it up to my professor and she said “I get what you mean but that’s not the point of the question. The point of the question is if you know which values of f(0) are guaranteed. 999999 is not guaranteed.” I told her that thats a completely different question than the one on the homework, which asks about “possible” values, not “guaranteed” values.

She didn’t respond to that, instead told me that if this question was impacting my grade at the end if the semester then we could revisit it. It’s not, so I’m not bugging my professor about it because she’s busy and there’s other students who need more help than I do.

But in any case, do you guys have any ideas about what I did wrong here?

Okay I’m really embarrassed to ask but I’m of an age(over 14) where I should know how to do some division but I can’t, every time someone tries to explain it to me it’s still hard for me to understand anything they say even if they yell at my face, so if you know how to do division can you please explain it to me because I’m really embarrassed by it and want to understand how to do division.

I don’t know if I should start with asking how to do division because I still don’t understand basic math but I want to learn.

Edit- Thank you to everyone that replied it kind of helped me understand:) I’m a very slow learner

I’ve only gone as far as Calc 3 and Linear Algebra so I’m somewhat familiar with like simple proofs and “showing” properties of spaces etc but…?

where did this rule come from? how does it make sense?

So im 13 and homeschooled. When I was younger my mom literally didnt teach me anything, not even how to write properly nor basic math, so I learned it really late....except I didnt, I was a stupid kid and didnt do my schoolwork so I didnt learn it, like some parts of addition that I dont have memorized or a bunch of numbers take me a while, fuck subtraction, I tried to teach myself multiplication and I cant get divion down, I was held back a grade, and i really need help, so please someone help me I dont know what to do, and self teaching something is very hard.

As my history shows, I post a lot here asking questions. It's being a great help at my learning. I'm doing all by my own without school or teachers, just a few books (which usually just give the final answer) and notepads, so whenever I can't get something, I post here.

Regardless of how casually you post here, thank you. It's being a great deal to me.

EDIT: after around two months of studying and asking questions here, I will be starting to learn calculus next week. I'm not sure if I'm ready to do so, but since I'm following the books from the same author, I will go on a limb and say that I am.

EDIT: aaand I finished the chapters about limits, derivatives and antiderivatives. I didn't go through any test, but I got the right answer on most exercises, so... Thank you very much for helping me on that.

I'm about to turn 18 and I'm way behind. I dropped out of high school and when I was in school I never tried. Because of this, I don't even know basic algebra. After studying for my GED I realized I actually like math and later decided I wanted to get a math degree.

I've gone back to Prealgebra and I've been studying it obsessively. I want to be able to get 100% on every test I take. I've been watching Professor Leonard and doing all his practice problems and taking notes. I feel like I'm not doing very well. I could do everything he says and follow all the steps but I wouldn't understand what I'm doing. I would be able to get the correct answer every time but not understand why the answer is correct. I don't want to know what to do. I want to know why that's what I'm supposed to do.

Do you guys have tips on how to understand math better? I don't just want the answers I want to truly understand it on a deep and meaningful level. I want to be able to look at a problem and figure it out because it makes sense to me not because I know the steps to solve it. I'm also interested how you guys study and learn math.

Title. I'm less concerned with the answer and more with how to figure it out. Thanks in advanced!

I'm thinking it would be 15 minutes * 1.25 because it's 25% longer? Which would be 18:45. Tho, I'm not sure if this is right.

So I noticed that all the math I learned up to lower division college math only goes to the 1700s. How much longer will it take to catch up to current math?

Do you all think this solution is good, or could it be tweaked/shortened? I'm being asked to give comments on how a student gave this solution.

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Hey guys, quick question, when doing sigma notation for series/sequences, can the n ever be a negative? Or must it always be positive? Thank you :)

I am a high school and have a huge passion for math ever since I was 5 years old. But a few years ago I found out about a problem I have : When I do math I almost totally lose the ability to make grammatically correct sentences, find my words or even pronounce words without stuttering. I’m not certain of the source of this problem but my theory is that it comes from the fact that I kind of stop thinking with words when I think in a mathematical way. I never paid much attentions to this because I usually am quiet, and I don’t remember having this problem when I was in middle school (might be because the math wasn’t challenging enough) but now it’s starting to affect my speech overall too, I use less and less words to think even when I’m not doing math. I’m posting this today because I was doing some heavy math at school for 2 hours straight and had a question to the teacher about the thing we were doing in math, and when I started talking I couldn’t even say a word correctly and was almost unable to explain what was bugging me. It might also be partly due to social anxiety but anyways, I desperately need tips to overcome this issue I have.

P.S : I apologize for the mistakes in this post, English is not my native language.

I feel like this is a simple question, but I'm not very certain about my reasoning, hence why I'm seeking help! Here goes:

If

x + 2y = 50

2x + 4y = 100

Is there any proof that x > y?

I have drawn out a graph and they are the same graph. So since when x is negative, y will definitely be larger than x, does it mean that there is no proof to proof that x > y?

I want to get better at math but I find myself asking for help with most questions I find difficult. Should I just not ask for help or what should I do to actually improve in solving math problems etc.

a) what is the probability he says yes?

I got this to be 2/3 from: 1/4 * 1/6 + 5/6 * 3/4

b) if he says yes what is the probability it is a six?

I'm unsure how to go from here, i thought maybe 1/4 * 2/3 * 1/6 but it seems to give the wrong answer

Hi, I'm an engineering student and I'm very good at math I have a 12 year old brother that is not very good and is struggling a lot, he basically has no idea, I been trying to help him learn but te thing is he doesn't have any of the concepts on his mind and he id completely lost, and I whenever we try to do his homework we lose a lot of time trying to explain the basics. I was wondering if someone here know about a book or a series of books with the math bases before algebra (because the school didn't even gave him a book, they just leave homework) so I can literally start from cero with a good structure?. Thanks for reading.

I'm making an infographic for fun to compare wealth by putting it in terms of distance.

If we equate $1 = 1 inch, then I want to confirm that the following calculations are true:

• the average U.S. salary of $40,000 is equivalent to 3,333 feet, or 0.631 miles

• the average lifetime earnings of an American are $1.7 million which is equivalent to 141,666.67 feet, or 26.830 miles

• Jeff Bezos' net worth is $196.7 billion, which is equivalent to 16,391,666,666.667 feet, or 3,104,482.32 miles.

Is this math correct?

The question has been answered. Thanks again to everyone that assisted me. Hello, everyone. I'm having some difficulty with this question.

How would find the limit of 1 + (8/9)^n?

I'm supposed to determine if the sequence converges and if it does, state the limit. I really don't know what to do.

Any number raised to infinity would most likely be infinity and 1 added to infinity would still be infinity right?

Then the sequence wouldn't be considered convergent because it doesn't end up at a fixed point but continues to infinity. I just wanna know if I'm thinking the right way. Thanks in advance (first time using reddit btw)

Hi! I am going crazy trying to make sense of this problem. I think I might be thinking “too far” on it because its difficulty really sticks out when compared to the material we’re currently working on. I really hate when I can’t solve things!

Here it is:

Kevin cleans his entire house in 30 minutes. Anna cleans the house in 60 minutes. How long would it take for them to clean it together?

I’ve been using fractions and piecing together that K cleans 2/3 when A cleans 1/3, stuff like that, but according to the solution key (which conveniently offers no walkthrough of the problem) the answer is 20 minutes. I’m frustrated beyond belief and I just can’t understand how the answer gets to be 20, even less when tasked with explaining that to my pupils.

So thankful for any help! 😊

I know this is super simple, but I’m just having a brain fart kind of day and none of the math I seem to do works out.

Let’s say there’s a lottery. Each ticket is $2, but only $1.5 goes towards the jackpot. Currently the total jackpot is $79.5. How many total tickets have been bought?

What I’ve done:

(79.5*0.25)+79.5 = 99.375 which gives an odd number, which can’t be correct since each ticket is $2.

(79.5/1.5) which I assumed would be total tickets, but 53 didn’t seem correct

I have a few questions that I'm really struggling on, I'm trying to Google the steps but I can't find what I need. I'm going to try and write out the questions and my confusion so please comment if you can help me with either one.

1. Lim x -> infinity (1-2x²⁾ ÷ (4x+3)² I understand limits that are approaching a real number, because I know you sub it in for x at some point, but im not sure what to sub in in place of infinity. Also, I'm not sure how to simplify the difference of squares more than just removing the squares, but then it just becomes (1-2x) ÷ (4x+3) which I also dont know what the next step is or if I can even simplify further.

Basically: what do you sub in for infinity? And: how do I simplify a difference of square being divided by another difference of square?

2. I have several practice questions like this: Y= (square root of (4x+3)) ÷ (2x) Or F(x)= x( 3 in the square root of (1-3x)) Or Y= square root over ALL (2+x) ÷ (2-x)

Basically: how do you find the derivitave of something without exponents, but with squares? Also in fractions? I only know polynomials.

If anyone has any advice on what may be a good step I'd appreciate it, after writing this out im wondering if I can convert the square roots into -2 exponents but that doesn't solve the fraction problem... im really not sure. Please let me know what you think.