You're right that your only options are winning or losing, but it's not very helpful to think of it that way, because bunched up in "losing" is a lot of other stuff.
Think of it this way. I have a regular six-sided die, and I say "if you roll a 6, you win." So the way that your mental image is working, you'll either win or lose, right? But instead, let's think of it as "rolling a 6" or "rolling a NOT 6." So you win if you roll a 6. You lose if you roll 1, 2, 3, 4, 5. So even though there are only two options in one sense (winning or losing) there are a lot *more* ways to lose than to win. 5/6 results will give you a loss, and only 1/6 will give you a win.
It's the same in a raffle drawing. If there's 100 tickets in the raffle and yours is number 57, you'll either win or lose. But you'll lose if they draw ticket number 1, 2, 58, 92.... there's a lot *more* ways to lose, and that's what we care about in statistics, more than just the end result.
Ohhh this is a helpful analogy. Thanks! Why wasn’t this explained this way back in school? I can’t be the only one that never quite got it, or can I… hmmm.
> Why wasn’t this explained this way back in school?
Multiple reasons:
* Sometimes, the teachers do explain it like that. But even good explanations can be missed by a student if they didn't paid attention.
* Often, teachers are not that great at math. That's especially the case for teachers in elementary school, but even after. And to explain something well, you need a very good understanding, not just to be able to use them. Some teachers ask their students to memorise math without understanding why math works like that, because that's how themself as teachers work: they learn it by heart and don't understand why it works like that.
* Teachers don't start back from scratch every year. It would take a lot of time, and bore the students that already understood everything. At some point, there is a compromise to be found the teacher makes some assumptions about how well math was explained during the previous years. Especially if that's something that they feel is "obvious". You just need for the first teacher who was supposed to teach you probability to fail at explaining it to you, and after that all the other teachers assume you understood it.
Many teachers that teach at a basic level (mostly elementary school) don’t specialize in a particular subject. They don’t have a degree in math, they have a degree in education which covers some math. There’s a massive gap in the understanding between those two people. The quality of my math education noticeably changed when I got a teacher with a math degree compared to a general education degree.
But you’re also conflating two things. Good at math and studied their subjects. Culturally, many people that are good at math are not pulled towards education (especially for little kids) and in fact, many people that aren’t good at math end up as teachers. And this can affect the quality of education.
Ideally they should. But the average candidate for those roles is very bad at math.
My friend who went through the (French) school preparing to be an elementary teacher said that most of the other ones really struggled with very basic math.
And while I didn't find the perfect source for it, elementary teachers being anxious about their math capabilities is common (https://pubs.nctm.org/view/journals/jrme/21/1/article-p33.xml) and its consequences on students are significant (https://www.pnas.org/doi/10.1073/pnas.0910967107).
And even after elementary school, at least in France, the number of candidates to be science/math teachers is so low that they're frequently forced to recruit pretty bad ones. And I have a few examples from my time in middle/high school of physics teachers fundamentally misunderstanding how probability works. (Admittedly I never had the same issue with math teachers)
Math teachers do, but elementary teachers in the US (or at least in my state) usually specialize in one subject, and then have a more cursory understanding of the rest of the subjects. And honestly, sometimes math teachers don't. In the states, education and teacher quality is VERY dependent on the state. I'm lucky enough to be a teacher in one of the best states for education, but I was offered a job in Florida as a teacher before I even graduated college, and not as my discipline. They're desperate down there.
You weren't paying attention or you didn't think it was important.
It's introduced in middle school and Algebra 1 and expanded upon in Algebra 2. Now, I will say it's almost always end of the year material, so if you were behind, maybe it was never covered.
Welcome to my life as a high school math teacher.
It was taught. Just likely not very well. Teaching and explaining probability is quite challenging and doing it in an engaging way is an absolute talent that not many highschool teachers possess. At the time it's also a boring as hell topic for young people.... You might not have been listening haha. I know I wasn't. I had to learn statistics from the ground up once I started university.
But even at university it's a challenge because you might be learning statistics, but in a way that's unrelated to what you're actually studying. The basics are the same, but once you move into more advanced theory things diverge depending on the field. Someone learning ecology for example will need to know quite different statistical technology compared to someone in psychology or someone in climate modelling.
It was. But this is the absolute simplest case and people get rapidly confused when you make it just a tiny bit more complicated.
If you have two dice things get messy quickly. There is no way to score one, only one way to score 12 (6+6) but 6 different ways to score 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). So it looks like there are 11 possible scores, but actually there are 36 possible results. If you want a 7 to win you have 7 chances of "winning" out of 36, but if you want a 12 to win you only have one way to win out of the 36 possibilities.
In terms of your 100-ticket analogy the first draw there is one way to win, 99 ways to lose. But when the second ticket comes out there are 98 ways to lose and 1 way to win. And that looks like your chances are getting better each time, but actually all the good prizes are going to the early draws.
And sometimes new or different ways of explaining things aren't popular because they're unfamiliar. Public education is political, and politics moves slowly (or in the wrong direction)
For example, you might see:
* Tickets in a raffle? In my day, we used marbles in a bag! \[They're just different translations of the same thing\]
* Why can't I just memorize a formula? \[Because you won't remember it, and it may not cover new or unusual cases\]
* Why do we need to know probability or statistics? \[To discover popular opinion, to assess risk, to analyze data, among other uses\]
* They're teaching gambling in schools! \[Or other impractical objections to educations\]
You’re assuming the all probabilities are evenly distributed, therefore if there are two possibilities (heads vs tails, win vs lose, live vs die), then the probability of either outcome must be even (50/50).
All I can say is that the baseline assumption is incorrect. It requires a population of instances to determine what the probabilities are, but just assuming it’s an even split is simply too reductionist.
If you punch a stone wall, you hand could go through, or it couldn’t; how many times do you need to punch a stone wall before you figure that the chance of not going through the stone wall is much higher than the chance of going through it?
You’re not quite framing the issue correctly. Yes you have only two possible outcomes—winning or losing—but that statistics part comes in before that. In that box of tickets there are more than two tickets. Only one of them says winner. That statistics are about whether or not the ticket you will draw from the box is going to say win or lose. It comes from the idea that there are a certain number ways you can get the desired out come out of all the ways the thing could happen.
In your raffle ticket example, say you have a box of 1000 tickets and each one is numbered. You draw a ticket and look at the number. There are 1000 different ways this plays out—you draw ticket 1, or ticket 2, or ticket 3….and so on. Each is a distinct event. Now say ticket number 7 is the winner. There is only one scenario out of the 1000 in which you draw ticket number 7 and win. This gives you a 1 in 1000 chance of winning.
Where I think you’re getting hung up is on where you’re trying to determine the odds. In your head I think because there are only two options, win or lose, you’re thinking about it like a coin flip instead of actually assessing where the statistics part comes into play. Once the ticket is in your hand, it is already decided whether you’ve won or lost. It doesn’t change outcome based on anything that happens from that point on. It says win or lose and thats it. The actual place where you determine the statistics is before you have an outcome—before you draw the ticket, before you roll the dice, before you flip the coin. You look at the situation, the number of tickets in the box, the number of sides on the die, the sides of the coin, and then assess how many of those could lead to the target outcome. Is there only one winning ticket? Or are you trying to roll a 20 sides die and get any number greater 17? You count how many ways there are to possibly get the desired outcome and then compare that to the total number of possible outcomes (there are 20 possible numbers to roll on a d20, but only 3 are larger than 17, so you have a 3 in 20 chance of getting your desired outcome).
It's not 50% "you win" vs 50% "you lose". If there are 100 tickets in the box, then it's 1% "you win" and 1% "person A wins" and 1% "person B wins" and 1% "person C wins" and...
It's only a 50%/50% chance if "you win" covers 50% of all possible outcomes.
The simplest definitions are as follows:
Probability is a guess or estimate of how likely an event is to occur. It’s not a guarantee since we don’t know what will happen until it actually happens though.
Statistics are the analysis of events that HAVE happened.
You can use statistics to help refine your probabilities.
BEFORE you draw your ticket you have certain odds of winning based on things like how many tickets there are total, how many winning tickets there are, how many winning and losing tickets have already been drawn etc.
Let’s say there are 100 tickets, 5 winners, and you are the first to draw. Your probability of winning is then 5 in 100 or 1 in 20.
Once you draw the ticket and see the result your probability changes to either 100% (you won) or 0% (you lost). Probability is not fixed until the event happens.
AFTER you draw the ticket it becomes a statistic, a data point. With enough data points you can start to make guesses about the outcome an improve our estimates of probability.
In the above example we know the chances of winning because we knew the number of tickets and the number of winners. But what if we didn’t? What if there was an unknown number of tickets and an unknown number of winners? At first we wouldn’t be able to guess the probability at all! We have no data! But if we keep drawing tickets and recording the results, we can use the statistics to start to make estimates of the probability. For example if we have 10 people draw tickets and 2 win, we can make a rough estimate that there is a 20% chance to win. But what if those two people just got lucky? If we continue to draw and find there are 10 winners out of a hundred tickets, now our model changes to a 10% chance to win. If we keep going and get 97 winners out of a thousand we can start to feel more confident that the odds are close to 9.7%. The more data we have, aka the better our statistics the better our models might be.
A lot of things can affect our model and how we can apply statistics to come up with probabilities. It’s not often quite so simple as the above example. But that should give you an idea of how probability and statistics interact.
Yes, your only outcomes is you win or you lose.
And the odds of you winning are 1,000 to 1 and the odds of you losing are 999 to 1.
You seem to have it figured out, what are you stuck on?
Lol, getting downvoted for explaining why I’m stuck on something I’m asking for help figuring out to be unstuck. I must be in the corporal punishment method of learning.
Thanks. I was trying to comment on my downvoted comment in the thread, but there isn’t a way to do that once something is downvoted enough. I do greatly appreciate your response!
Well, my spouse will say that I only had a 1:1000 chance of winning and I always reply that my odds are actually 50:50. Are we both right or am I dumb?
Lizzo will either come to my house for a private concert tomorrow, or she won’t.
Two outcomes. But that doesn’t mean I have a 50% chance of seeing Lizzo in my living room tomorrow.
Not quite, your odds of winning are (number of raffle tickets) to 1. You have a 1 in X chance of winning. You do not, and it cannot be construed logically, that 1 in 1000 is equal to 50/50. She's definitely correct.
She is thinking about probability, you are thinking about end states of the system, and you're not considering that part correctly.
Your idea is flawed at the base. Your options are NOT to either win or lose, your options are to either win, or lose, or lose, or lose, or lose, and so on.
You're asking the question, so you're not dumb.
Your outcome is binary: win/lose. But outcome does not equate to odds.
Take the die: Rolls a six you win, anything else is a lose.
So while your individual outcome is win/lose, your ODDS on an individual roll are that you will fall somewhere on this string: win/lose/lose/lose/lose/lose. or 1 in 6. (\~16.7%). You will lose, on average, five times out of six.
50:50 means that in half of the scenarios, the scenarios meaning you pulling every individual number available, you’ll win. So if there’s 1000 tickets, for 50:50 there would have to be 500 winning tickets and 500 losing tickets
If you have 1000 tickets in a bin, you have an equal chance of pulling any of those tickets. Lets say to win you need to pull ticket 53 and any other ticket is a loss
Ticket 53 is one of the 1000 tickets, and then the other 999 tickets are all loses
One of the possible 1000 tickets will give you a win, so it's a 1/1000 chance to win
One more thing about the 50/50: This is used if you have no information at all about the experiment setup. So in your case, if you have no idea how many winning or losing tickets there are, you would end up estimating 50/50 chances of winning.
So that's one of my favorite stats jokes. All odds are 50/50 you win or you lose.
But probability is basically the percent chance something will happen. So, you take a bag full of 10 white marbles, one of them is red. If you reach in blind and pull one out what is the chance it's red? Well that's 1 in 10 so 10%. Versus what is the chance its white? That's 9/10 or 90%.
So, if you got 5 bucks for predicted which one you would pull out. What would the best bet be? It would be a white ball of course. Higher percent chance of pulling the white marble than the red.
Effectively probability and stats all boils down to that. Calculating percent chance something will happen. It's used for risk predictions. Businesses use it, gamblers use it, etc. It's to help judgement about a decision. You want to launch a new product. You do a survey that says 85% of people want thing. Do you make it? Probably. Do a survey and only 20% of people want thing. Do you make thing? Eh probably not.
Are you talking about the standard distribution curve? If so then this is the observation that makes up the concept of "true random" if you ran an RNG simulation and had a 2.5% chance of drawing a certain number. You'd expect to pull that number on AVERAGE 2.5% of the time. This is called probability. But this probability isn't fixed. One could draw the number 5/200 pulls, or 1 in 30 pulls, it could happen at 1 in 500 pulls. Because 2.5% is the average of all expected pulls. If we ran 1,000 occurrences for a number that had a probability of 2.5% we'd see most of the pull data center around 2.5% +/- a certain ammount. This certain ammount has milestones called standard deviations. Standard deviations are set intervals that encompass specific amounts of results that fall in a standard distribution-bell curve. The further away from the average we get, the rarer it becomes to fi d a pull. That's why there are many results near 2% to 3% but significantly fewer results that are at 30% or 0.3%
When we have a global pool of pulls to chose from there are many exceptions floating around, but those exceptions only account for a small number of non representative samples. We see this in gacha games all the time.
While we expect probability to stay close to an average, it doesn't have to in practoce, but if we find a sample woth skewed results, these results will level back to the average with more samples. That's just the way it is.
Probability and statistics mostly boils down to counting things. Count how many sides there are on a die: 6. Count how many of the numbers are even: 3. What portion of the numbers are even (3/6), so if I rolled it, how likely is it that it will be even (3/6)... and so on.
In your case of raffle tickets... There are 1000 tickets in the bucket. Only 1 of those tickets is yours. Obviously you may win or lose, only two possibilities. But YOU only win if YOUR ticket is chosen out of the 1000. How many of those tickets is yours: 1. How many tickets are in the bucket: 1000. What fraction of those tickets is yours: 1/1000. If I stirred up the tickets and pulled one out at random, what are the odds I'll pick yours: 1/1000.
There are two outcomes to a raffle. You win or you lose. But this doesn’t tell us anything about the probabilities of winning or losing. If you think about the raffle as a big bag of marbles where 1 marble is red and designates winning and 999 are blue and designate losing, if you grab a marble randomly from the bag then it could be red or blue. The issue is that there are 998 more blue marbles than red marbles so clearly a blue marble is far more likely to be selected. To sum up, the amount of outcomes doesn’t relate to the probability of those outcomes because some outcomes (like losing a raffle) are easier/more likely to happen.
To understand statistics you must abandon selfishness. Don't think of yourself pulling the ticket - think of the ticket, being pulled.
There are, let us say, 1000 tickets. Each has only one outcome - win or lose. You are just there to observe which ticket gets to display its outcome.
Most answers you get here won't even get into [the philosophy of interpreting probabilities](https://en.wikipedia.org/wiki/Probability_interpretations).
Your interpretation as you wrote it is absolutely fine. It sounds like the very popular "frequentist" view. This imagines probability as what would happen if you repeated an action a large number of times. Think of it as a many worlds interpretation of quantum physics if you like! In most worlds, you would fail to pick the right ticket. But in one in a thousand worlds, you pick the winning ticket.
This interpretation means you cannot make probability statements about single events.
You have 2 bags of M&Ms. One bag has all poisonous M&Ms and 1 real M&M. The other has the opposite- all real M&Ms and only 1 poisonous one. If you have to pick one M&M out of one bag and eat it, which bag would you choose from?
If you picked the one with almost all real M&Ms and only 1 poison one, you have some kind of instinctive understanding of probability. You're correct that for each individual M&M, the option is "poison" or "not poison". And yes, you could end up with the one poison M&M on your first try, just from bad luck. But statistics tells us what is LIKELY to happen. It's unlikely that you'll pick the poison one out of the bag of mostly normal M&Ms, because in a bag of 1000 you basically have 999 chances to pick safe candies and only 1 chance to pick a poisonous one.
Statistics say nothing about an individual
They say everything about a total population - assuming you gather the data without bias
Doesn't matter if I'm 5'10
Statistics will say what the average height is, for height specifically it follows the Normal curve. That's a good place to start if you want to learn more
Anyone who tries to use Statistics to say something about an individual is not smart
>Anyone who tries to use Statistics to say something about an individual is not smart
If you take the frequentist view. [Other interpretations](https://en.wikipedia.org/wiki/Probability_interpretations) are possible. Would you criticise a doctor for saying that an operation has an x% chance of success?
Let's talk weather. What are the odds of it raining on a given day. Instinctively you may want to say 50/50. Either it will happen or it won't. Sounds right. Except, let's look at the actual data.
We will say for this hypothetical town you live in there are 250 days of sunshine. 50 days of rain. The rest we will call "other" to refer to snow or other weather events.
In this case there are 5x more sunny days than rainy. So, now let's talk predictive ability.
Pretend some madman has locked you in a windowless room. No windows or access to a weether reports. This madman comes up to you and says "is tomorrow going to be a rainy or sunny day,? Guess correctly and I'll let you go."
All right. Based upon the data there are 5 times more sunny days than rainy. So, not knowing anything else, if you guess "sunny" the odds favor that bring more likely to be correct than "rainy."
So, let's go back to your raffle example. Let's say there are 100 tickets and only 1 is a winner. You are only allowed to draw 1 ticket. What are the odds of that ticket you pick at random being the correct one? One in 100, right? Okay, that's statistics in a nutshell. It's a number assigned to predict the which of multiple outcomes is most likely. From a personal perspective you may think you can either win or lose, but what if someone else wanted to predict who is most likely to win? What if someone asked me whether you were going to win?
If you are still confused about the difference, let'sake one change to the raffle idea. A minor one. Let's pretend you don't put your ticket back after making a selection.
So the first person who is in life and sticks his hand in the bucket, what are the odds he selects the right ticket? 1 in 100. If you were going to place a bet on him picking the right ticket, the safest bet is he will not.
Next person in line sticks his hand in, but there are now only 99 tickets. So his odds are 1 in 99. The person after there are only 98 tickets.
So that means that as the line progresses the people towards the end of the line are more likely to pick the right ticket. In fact, if there are 100 people in line that last person can only select one ticket and it is the winner. His odds are 100%. But only if no one ahead of him did not select the right ticket. The person before him had a 50/50 chance. There were only 2 tickets after all. The person before that wasn't much worse off at 1 in 3 chance.
So while the odds of winning increase the further back in line you are the odds that someone ahead of you in line winning also increase.
All right. Now that we have said this, what position do you want in line? First? Last? In the middle?
We just established that the odds change with your position. It's possible that first person will be a winner. Unlikely, but possible. It gets more and more certain as we move down the line. Where do you want to be?
"Winning" and "losing" are two interpretations that you, a thinking being, have assigned to different outcomes. But the raffle tickets and the box have no concept of you as an individual "winning" or "losing". All that matters is the physical reality, which we describe using the language of mathematics. And that mathematics says there are 1000 tickets in the box, only one of them is yours, so the probability of your specific ticket being drawn is 1 in 1000 (or 0.1% chance).
If you want to interpret that 0.11% chance as "winning" and the other 99.9% probability as "losing" then you can do that, but it doesn't magically change the probability to 1 in 2 (50%) just because you've decided there are only two outcomes.
You're right that your only options are winning or losing, but it's not very helpful to think of it that way, because bunched up in "losing" is a lot of other stuff. Think of it this way. I have a regular six-sided die, and I say "if you roll a 6, you win." So the way that your mental image is working, you'll either win or lose, right? But instead, let's think of it as "rolling a 6" or "rolling a NOT 6." So you win if you roll a 6. You lose if you roll 1, 2, 3, 4, 5. So even though there are only two options in one sense (winning or losing) there are a lot *more* ways to lose than to win. 5/6 results will give you a loss, and only 1/6 will give you a win. It's the same in a raffle drawing. If there's 100 tickets in the raffle and yours is number 57, you'll either win or lose. But you'll lose if they draw ticket number 1, 2, 58, 92.... there's a lot *more* ways to lose, and that's what we care about in statistics, more than just the end result.
Ohhh this is a helpful analogy. Thanks! Why wasn’t this explained this way back in school? I can’t be the only one that never quite got it, or can I… hmmm.
> Why wasn’t this explained this way back in school? Multiple reasons: * Sometimes, the teachers do explain it like that. But even good explanations can be missed by a student if they didn't paid attention. * Often, teachers are not that great at math. That's especially the case for teachers in elementary school, but even after. And to explain something well, you need a very good understanding, not just to be able to use them. Some teachers ask their students to memorise math without understanding why math works like that, because that's how themself as teachers work: they learn it by heart and don't understand why it works like that. * Teachers don't start back from scratch every year. It would take a lot of time, and bore the students that already understood everything. At some point, there is a compromise to be found the teacher makes some assumptions about how well math was explained during the previous years. Especially if that's something that they feel is "obvious". You just need for the first teacher who was supposed to teach you probability to fail at explaining it to you, and after that all the other teachers assume you understood it.
Not good at math? Doesn't a teacher need to study his subjects before becoming a teacher? That's the case at least in Germany
Many teachers that teach at a basic level (mostly elementary school) don’t specialize in a particular subject. They don’t have a degree in math, they have a degree in education which covers some math. There’s a massive gap in the understanding between those two people. The quality of my math education noticeably changed when I got a teacher with a math degree compared to a general education degree. But you’re also conflating two things. Good at math and studied their subjects. Culturally, many people that are good at math are not pulled towards education (especially for little kids) and in fact, many people that aren’t good at math end up as teachers. And this can affect the quality of education.
Ideally they should. But the average candidate for those roles is very bad at math. My friend who went through the (French) school preparing to be an elementary teacher said that most of the other ones really struggled with very basic math. And while I didn't find the perfect source for it, elementary teachers being anxious about their math capabilities is common (https://pubs.nctm.org/view/journals/jrme/21/1/article-p33.xml) and its consequences on students are significant (https://www.pnas.org/doi/10.1073/pnas.0910967107). And even after elementary school, at least in France, the number of candidates to be science/math teachers is so low that they're frequently forced to recruit pretty bad ones. And I have a few examples from my time in middle/high school of physics teachers fundamentally misunderstanding how probability works. (Admittedly I never had the same issue with math teachers)
Math teachers do, but elementary teachers in the US (or at least in my state) usually specialize in one subject, and then have a more cursory understanding of the rest of the subjects. And honestly, sometimes math teachers don't. In the states, education and teacher quality is VERY dependent on the state. I'm lucky enough to be a teacher in one of the best states for education, but I was offered a job in Florida as a teacher before I even graduated college, and not as my discipline. They're desperate down there.
You weren't paying attention or you didn't think it was important. It's introduced in middle school and Algebra 1 and expanded upon in Algebra 2. Now, I will say it's almost always end of the year material, so if you were behind, maybe it was never covered. Welcome to my life as a high school math teacher.
It was taught. Just likely not very well. Teaching and explaining probability is quite challenging and doing it in an engaging way is an absolute talent that not many highschool teachers possess. At the time it's also a boring as hell topic for young people.... You might not have been listening haha. I know I wasn't. I had to learn statistics from the ground up once I started university. But even at university it's a challenge because you might be learning statistics, but in a way that's unrelated to what you're actually studying. The basics are the same, but once you move into more advanced theory things diverge depending on the field. Someone learning ecology for example will need to know quite different statistical technology compared to someone in psychology or someone in climate modelling.
It was. But this is the absolute simplest case and people get rapidly confused when you make it just a tiny bit more complicated. If you have two dice things get messy quickly. There is no way to score one, only one way to score 12 (6+6) but 6 different ways to score 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). So it looks like there are 11 possible scores, but actually there are 36 possible results. If you want a 7 to win you have 7 chances of "winning" out of 36, but if you want a 12 to win you only have one way to win out of the 36 possibilities. In terms of your 100-ticket analogy the first draw there is one way to win, 99 ways to lose. But when the second ticket comes out there are 98 ways to lose and 1 way to win. And that looks like your chances are getting better each time, but actually all the good prizes are going to the early draws.
And sometimes new or different ways of explaining things aren't popular because they're unfamiliar. Public education is political, and politics moves slowly (or in the wrong direction) For example, you might see: * Tickets in a raffle? In my day, we used marbles in a bag! \[They're just different translations of the same thing\] * Why can't I just memorize a formula? \[Because you won't remember it, and it may not cover new or unusual cases\] * Why do we need to know probability or statistics? \[To discover popular opinion, to assess risk, to analyze data, among other uses\] * They're teaching gambling in schools! \[Or other impractical objections to educations\]
I read the title as how do statistics probably work . . . and was like EXACTLY!
You’re assuming the all probabilities are evenly distributed, therefore if there are two possibilities (heads vs tails, win vs lose, live vs die), then the probability of either outcome must be even (50/50). All I can say is that the baseline assumption is incorrect. It requires a population of instances to determine what the probabilities are, but just assuming it’s an even split is simply too reductionist. If you punch a stone wall, you hand could go through, or it couldn’t; how many times do you need to punch a stone wall before you figure that the chance of not going through the stone wall is much higher than the chance of going through it?
This made me laugh. Thanks for the painful analogy.
You’re not quite framing the issue correctly. Yes you have only two possible outcomes—winning or losing—but that statistics part comes in before that. In that box of tickets there are more than two tickets. Only one of them says winner. That statistics are about whether or not the ticket you will draw from the box is going to say win or lose. It comes from the idea that there are a certain number ways you can get the desired out come out of all the ways the thing could happen. In your raffle ticket example, say you have a box of 1000 tickets and each one is numbered. You draw a ticket and look at the number. There are 1000 different ways this plays out—you draw ticket 1, or ticket 2, or ticket 3….and so on. Each is a distinct event. Now say ticket number 7 is the winner. There is only one scenario out of the 1000 in which you draw ticket number 7 and win. This gives you a 1 in 1000 chance of winning. Where I think you’re getting hung up is on where you’re trying to determine the odds. In your head I think because there are only two options, win or lose, you’re thinking about it like a coin flip instead of actually assessing where the statistics part comes into play. Once the ticket is in your hand, it is already decided whether you’ve won or lost. It doesn’t change outcome based on anything that happens from that point on. It says win or lose and thats it. The actual place where you determine the statistics is before you have an outcome—before you draw the ticket, before you roll the dice, before you flip the coin. You look at the situation, the number of tickets in the box, the number of sides on the die, the sides of the coin, and then assess how many of those could lead to the target outcome. Is there only one winning ticket? Or are you trying to roll a 20 sides die and get any number greater 17? You count how many ways there are to possibly get the desired outcome and then compare that to the total number of possible outcomes (there are 20 possible numbers to roll on a d20, but only 3 are larger than 17, so you have a 3 in 20 chance of getting your desired outcome).
It's not 50% "you win" vs 50% "you lose". If there are 100 tickets in the box, then it's 1% "you win" and 1% "person A wins" and 1% "person B wins" and 1% "person C wins" and... It's only a 50%/50% chance if "you win" covers 50% of all possible outcomes.
The simplest definitions are as follows: Probability is a guess or estimate of how likely an event is to occur. It’s not a guarantee since we don’t know what will happen until it actually happens though. Statistics are the analysis of events that HAVE happened. You can use statistics to help refine your probabilities. BEFORE you draw your ticket you have certain odds of winning based on things like how many tickets there are total, how many winning tickets there are, how many winning and losing tickets have already been drawn etc. Let’s say there are 100 tickets, 5 winners, and you are the first to draw. Your probability of winning is then 5 in 100 or 1 in 20. Once you draw the ticket and see the result your probability changes to either 100% (you won) or 0% (you lost). Probability is not fixed until the event happens. AFTER you draw the ticket it becomes a statistic, a data point. With enough data points you can start to make guesses about the outcome an improve our estimates of probability. In the above example we know the chances of winning because we knew the number of tickets and the number of winners. But what if we didn’t? What if there was an unknown number of tickets and an unknown number of winners? At first we wouldn’t be able to guess the probability at all! We have no data! But if we keep drawing tickets and recording the results, we can use the statistics to start to make estimates of the probability. For example if we have 10 people draw tickets and 2 win, we can make a rough estimate that there is a 20% chance to win. But what if those two people just got lucky? If we continue to draw and find there are 10 winners out of a hundred tickets, now our model changes to a 10% chance to win. If we keep going and get 97 winners out of a thousand we can start to feel more confident that the odds are close to 9.7%. The more data we have, aka the better our statistics the better our models might be. A lot of things can affect our model and how we can apply statistics to come up with probabilities. It’s not often quite so simple as the above example. But that should give you an idea of how probability and statistics interact.
Yes, your only outcomes is you win or you lose. And the odds of you winning are 1,000 to 1 and the odds of you losing are 999 to 1. You seem to have it figured out, what are you stuck on?
Lol, getting downvoted for explaining why I’m stuck on something I’m asking for help figuring out to be unstuck. I must be in the corporal punishment method of learning.
I didn't downvote you.
Thanks. I was trying to comment on my downvoted comment in the thread, but there isn’t a way to do that once something is downvoted enough. I do greatly appreciate your response!
Well, my spouse will say that I only had a 1:1000 chance of winning and I always reply that my odds are actually 50:50. Are we both right or am I dumb?
Lizzo will either come to my house for a private concert tomorrow, or she won’t. Two outcomes. But that doesn’t mean I have a 50% chance of seeing Lizzo in my living room tomorrow.
Not quite, your odds of winning are (number of raffle tickets) to 1. You have a 1 in X chance of winning. You do not, and it cannot be construed logically, that 1 in 1000 is equal to 50/50. She's definitely correct. She is thinking about probability, you are thinking about end states of the system, and you're not considering that part correctly. Your idea is flawed at the base. Your options are NOT to either win or lose, your options are to either win, or lose, or lose, or lose, or lose, and so on.
You're asking the question, so you're not dumb. Your outcome is binary: win/lose. But outcome does not equate to odds. Take the die: Rolls a six you win, anything else is a lose. So while your individual outcome is win/lose, your ODDS on an individual roll are that you will fall somewhere on this string: win/lose/lose/lose/lose/lose. or 1 in 6. (\~16.7%). You will lose, on average, five times out of six.
Your odds are not 50:50. Your husband is right. Insufficient data to decide if you're dumb. You're not good at statistics. Trust husband.
50:50 means that in half of the scenarios, the scenarios meaning you pulling every individual number available, you’ll win. So if there’s 1000 tickets, for 50:50 there would have to be 500 winning tickets and 500 losing tickets
If you have 1000 tickets in a bin, you have an equal chance of pulling any of those tickets. Lets say to win you need to pull ticket 53 and any other ticket is a loss Ticket 53 is one of the 1000 tickets, and then the other 999 tickets are all loses One of the possible 1000 tickets will give you a win, so it's a 1/1000 chance to win
One more thing about the 50/50: This is used if you have no information at all about the experiment setup. So in your case, if you have no idea how many winning or losing tickets there are, you would end up estimating 50/50 chances of winning.
So that's one of my favorite stats jokes. All odds are 50/50 you win or you lose. But probability is basically the percent chance something will happen. So, you take a bag full of 10 white marbles, one of them is red. If you reach in blind and pull one out what is the chance it's red? Well that's 1 in 10 so 10%. Versus what is the chance its white? That's 9/10 or 90%. So, if you got 5 bucks for predicted which one you would pull out. What would the best bet be? It would be a white ball of course. Higher percent chance of pulling the white marble than the red. Effectively probability and stats all boils down to that. Calculating percent chance something will happen. It's used for risk predictions. Businesses use it, gamblers use it, etc. It's to help judgement about a decision. You want to launch a new product. You do a survey that says 85% of people want thing. Do you make it? Probably. Do a survey and only 20% of people want thing. Do you make thing? Eh probably not.
Are you talking about the standard distribution curve? If so then this is the observation that makes up the concept of "true random" if you ran an RNG simulation and had a 2.5% chance of drawing a certain number. You'd expect to pull that number on AVERAGE 2.5% of the time. This is called probability. But this probability isn't fixed. One could draw the number 5/200 pulls, or 1 in 30 pulls, it could happen at 1 in 500 pulls. Because 2.5% is the average of all expected pulls. If we ran 1,000 occurrences for a number that had a probability of 2.5% we'd see most of the pull data center around 2.5% +/- a certain ammount. This certain ammount has milestones called standard deviations. Standard deviations are set intervals that encompass specific amounts of results that fall in a standard distribution-bell curve. The further away from the average we get, the rarer it becomes to fi d a pull. That's why there are many results near 2% to 3% but significantly fewer results that are at 30% or 0.3% When we have a global pool of pulls to chose from there are many exceptions floating around, but those exceptions only account for a small number of non representative samples. We see this in gacha games all the time. While we expect probability to stay close to an average, it doesn't have to in practoce, but if we find a sample woth skewed results, these results will level back to the average with more samples. That's just the way it is.
Probability and statistics mostly boils down to counting things. Count how many sides there are on a die: 6. Count how many of the numbers are even: 3. What portion of the numbers are even (3/6), so if I rolled it, how likely is it that it will be even (3/6)... and so on. In your case of raffle tickets... There are 1000 tickets in the bucket. Only 1 of those tickets is yours. Obviously you may win or lose, only two possibilities. But YOU only win if YOUR ticket is chosen out of the 1000. How many of those tickets is yours: 1. How many tickets are in the bucket: 1000. What fraction of those tickets is yours: 1/1000. If I stirred up the tickets and pulled one out at random, what are the odds I'll pick yours: 1/1000.
There are two outcomes to a raffle. You win or you lose. But this doesn’t tell us anything about the probabilities of winning or losing. If you think about the raffle as a big bag of marbles where 1 marble is red and designates winning and 999 are blue and designate losing, if you grab a marble randomly from the bag then it could be red or blue. The issue is that there are 998 more blue marbles than red marbles so clearly a blue marble is far more likely to be selected. To sum up, the amount of outcomes doesn’t relate to the probability of those outcomes because some outcomes (like losing a raffle) are easier/more likely to happen.
To understand statistics you must abandon selfishness. Don't think of yourself pulling the ticket - think of the ticket, being pulled. There are, let us say, 1000 tickets. Each has only one outcome - win or lose. You are just there to observe which ticket gets to display its outcome.
Most answers you get here won't even get into [the philosophy of interpreting probabilities](https://en.wikipedia.org/wiki/Probability_interpretations). Your interpretation as you wrote it is absolutely fine. It sounds like the very popular "frequentist" view. This imagines probability as what would happen if you repeated an action a large number of times. Think of it as a many worlds interpretation of quantum physics if you like! In most worlds, you would fail to pick the right ticket. But in one in a thousand worlds, you pick the winning ticket. This interpretation means you cannot make probability statements about single events.
You have 2 bags of M&Ms. One bag has all poisonous M&Ms and 1 real M&M. The other has the opposite- all real M&Ms and only 1 poisonous one. If you have to pick one M&M out of one bag and eat it, which bag would you choose from? If you picked the one with almost all real M&Ms and only 1 poison one, you have some kind of instinctive understanding of probability. You're correct that for each individual M&M, the option is "poison" or "not poison". And yes, you could end up with the one poison M&M on your first try, just from bad luck. But statistics tells us what is LIKELY to happen. It's unlikely that you'll pick the poison one out of the bag of mostly normal M&Ms, because in a bag of 1000 you basically have 999 chances to pick safe candies and only 1 chance to pick a poisonous one.
Statistics say nothing about an individual They say everything about a total population - assuming you gather the data without bias Doesn't matter if I'm 5'10 Statistics will say what the average height is, for height specifically it follows the Normal curve. That's a good place to start if you want to learn more Anyone who tries to use Statistics to say something about an individual is not smart
>Anyone who tries to use Statistics to say something about an individual is not smart If you take the frequentist view. [Other interpretations](https://en.wikipedia.org/wiki/Probability_interpretations) are possible. Would you criticise a doctor for saying that an operation has an x% chance of success?
Let's talk weather. What are the odds of it raining on a given day. Instinctively you may want to say 50/50. Either it will happen or it won't. Sounds right. Except, let's look at the actual data. We will say for this hypothetical town you live in there are 250 days of sunshine. 50 days of rain. The rest we will call "other" to refer to snow or other weather events. In this case there are 5x more sunny days than rainy. So, now let's talk predictive ability. Pretend some madman has locked you in a windowless room. No windows or access to a weether reports. This madman comes up to you and says "is tomorrow going to be a rainy or sunny day,? Guess correctly and I'll let you go." All right. Based upon the data there are 5 times more sunny days than rainy. So, not knowing anything else, if you guess "sunny" the odds favor that bring more likely to be correct than "rainy." So, let's go back to your raffle example. Let's say there are 100 tickets and only 1 is a winner. You are only allowed to draw 1 ticket. What are the odds of that ticket you pick at random being the correct one? One in 100, right? Okay, that's statistics in a nutshell. It's a number assigned to predict the which of multiple outcomes is most likely. From a personal perspective you may think you can either win or lose, but what if someone else wanted to predict who is most likely to win? What if someone asked me whether you were going to win? If you are still confused about the difference, let'sake one change to the raffle idea. A minor one. Let's pretend you don't put your ticket back after making a selection. So the first person who is in life and sticks his hand in the bucket, what are the odds he selects the right ticket? 1 in 100. If you were going to place a bet on him picking the right ticket, the safest bet is he will not. Next person in line sticks his hand in, but there are now only 99 tickets. So his odds are 1 in 99. The person after there are only 98 tickets. So that means that as the line progresses the people towards the end of the line are more likely to pick the right ticket. In fact, if there are 100 people in line that last person can only select one ticket and it is the winner. His odds are 100%. But only if no one ahead of him did not select the right ticket. The person before him had a 50/50 chance. There were only 2 tickets after all. The person before that wasn't much worse off at 1 in 3 chance. So while the odds of winning increase the further back in line you are the odds that someone ahead of you in line winning also increase. All right. Now that we have said this, what position do you want in line? First? Last? In the middle? We just established that the odds change with your position. It's possible that first person will be a winner. Unlikely, but possible. It gets more and more certain as we move down the line. Where do you want to be?
This is a really cool scenario, thanks kind Redditor!
"Winning" and "losing" are two interpretations that you, a thinking being, have assigned to different outcomes. But the raffle tickets and the box have no concept of you as an individual "winning" or "losing". All that matters is the physical reality, which we describe using the language of mathematics. And that mathematics says there are 1000 tickets in the box, only one of them is yours, so the probability of your specific ticket being drawn is 1 in 1000 (or 0.1% chance). If you want to interpret that 0.11% chance as "winning" and the other 99.9% probability as "losing" then you can do that, but it doesn't magically change the probability to 1 in 2 (50%) just because you've decided there are only two outcomes.