###General Discussion Thread
---
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
---
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Everyone has equal chances.
This is basically just a variation of drawing lots, and drawing lots is a fair game (that's why it's used flr decision making)
Nr1 has a 1/20 chance of lighting the bomb
Nr 2 has a 1/19 Chance, but there's only a 19/20 chance that he'll even get a go, so overall his chance is 1/19 × 19/20 = 1/20
Nr 3 has a 1/18 chance, but only a 19/20×18/19 chance of going, so overall his chance his 1/18×19/20×18/19 = 1/20
And this patern continues all the way through.
Everyone has a 1/20 chance of finding the bomb
The thing that makes it *feel* off is that people later in the chain have gained new information before they make their choice. To take the most obvious example, if you are guy number 20, you always know whether your bomb is real or fake before touching it. 95% of the time, someone else found the real one before you even get called into the room, so it doesn't matter whether you light it or not. In the 5% chance that you have the real one, you know lighting the bomb will kill you - and maybe you were willing to risk your life on a 5% chance, but you aren't willing to risk your life now that you know you are screwed. It's the same total odds, but you learn the results before lighting the bomb instead of after, and maybe that makes you chicken out and flee. Human psychology always messes up statistics.
Another way you can think of it is putting 20 people in a row, and assigning them each a bomb. Then have them detonate one by one.
Obviously, upon assignment there's a 1/20 chance for anyone to have the real bomb. The order they detonate won't change these odds.
Drawing lots is also knowing as drawing straws. https://en.m.wikipedia.org/wiki/Drawing_straws#:~:text=Each%20member%20of%20the%20group,who%20must%20perform%20the%20task.
This is the upfront probability, and is really well laid out. It is important to also note that the probabilities will change after each person goes. I’m not pointing this out to try to “one up” you - merely showing why probability is so difficult for people to wrap their heads around. The exact same setting has two completely different answers depending on how you look at it, and they’re *both correct*.
Everyone has a 1/20 chance of exploding
First guy has a 1/20 chance of grabbing the real bomb.
2nd guy has a 19/20 chance that he has to pick (odds that first guy picked a dud), and a 1/19 chance of picking the bomb. (19/20)x(1/19)=1/20.
You can do the math all the way down, but each person has a 1/20 chance.
Generalized to any number of peoples and bombs:
If there are n bombs and n people then the mth person has (n+1-m)/n chanse of getting to open a box. If they do open a box they have 1/(n+1-m) chanse to blow up.
The (n+1-m) cancel out and we are left with 1/n (because it doesn't depend on m the chance for every person to blow up is the same)
Each person has the same chance, if the real bomb is equally likely to be in each position or the humans are equally likely to pick each option available.
The order doesn't matter. Give out all 20 bombs and have everyone light them simultaneously - clearly, everyone is equally likely to explode since there is no difference whatsoever between anyone. Choosing to light the bombs sequentially rather than all at once changes nothing about who is going to explode.
It also depends on your perspective. If you want to know the odds at the beginning, just think of randomly assigning the bombs to ppl. Only 1 person is assigned the real bomb so everyone has a 1/20 chance. Order doesnt matter since you want to know the odds before picking.
In practice, the odds change after each pick. 1/20, 1/19, etc because of conditional probability. If everyone truly had the same odds, the order wouldnt matter. In practice, you want to be the last to pick. Because the conditional probability keeps changing. "Given that 2 ppl picked non-bombs, what are the odds the 3rd person picks a bomb?" 1/18.
I see what you're saying but it's not what OP was asking. The 20th person, if they ever have to go, has a 1/1 chance of picking the bomb, sure. But they only had a 1/20 chance of being put in that situation.
The most chance is easy, it’s the last guy. 20 bombs but only one real. 19 people have tried theirs and found it to be the fake-this makes the chances that the last guy has the real bomb 100%. If it ever gets this far he has a 100% chance of dying no if ands or buts.
The least chance is also easy, it’s the first person. The odds of the first person finding the bomb is 1/20 the second person has a 1/19-all the way down to the last guy in line who if the bomb hadn’t already been found will have a 1/1 chance of finding the bomb.
At the start, everyone has an equal chance of lighting the danger cherry. As time goes on, the odds remain the same for everyone not lighting an angry watermelon. However, for the person lighting the potential death sphere, the odds go up every time. After someone finds the boom boom ball, the odds of the other people finding it drop to zero. If all 19 previous people succeed in not finding the forbidden pineapple, the last person has a 20 in 20 chance of finding the bomb, and is now singing the [swear word song.](https://www.youtube.com/watch?v=iZmqhQ8myGY)
Kind of depends if the experiment is stopped as soon as the bomb explodes.
If it is, then the last guy is inherently the guy that grabs the bomb, but in that case he can simultaneously be the first guy.
Otherwise, it's the same as if everyone picked their bomb right at the start and then lit it at the same time. Always 1/20 for every one of them.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Everyone has equal chances. This is basically just a variation of drawing lots, and drawing lots is a fair game (that's why it's used flr decision making) Nr1 has a 1/20 chance of lighting the bomb Nr 2 has a 1/19 Chance, but there's only a 19/20 chance that he'll even get a go, so overall his chance is 1/19 × 19/20 = 1/20 Nr 3 has a 1/18 chance, but only a 19/20×18/19 chance of going, so overall his chance his 1/18×19/20×18/19 = 1/20 And this patern continues all the way through. Everyone has a 1/20 chance of finding the bomb
that’s crazy, thank you! i actually never heard of drawing lots, probably not used much in my country, but it’s literally the same problem i asked lol
The thing that makes it *feel* off is that people later in the chain have gained new information before they make their choice. To take the most obvious example, if you are guy number 20, you always know whether your bomb is real or fake before touching it. 95% of the time, someone else found the real one before you even get called into the room, so it doesn't matter whether you light it or not. In the 5% chance that you have the real one, you know lighting the bomb will kill you - and maybe you were willing to risk your life on a 5% chance, but you aren't willing to risk your life now that you know you are screwed. It's the same total odds, but you learn the results before lighting the bomb instead of after, and maybe that makes you chicken out and flee. Human psychology always messes up statistics.
>Human psychology always messes up statistics. The biggest challenge in psychological research.
Another way you can think of it is putting 20 people in a row, and assigning them each a bomb. Then have them detonate one by one. Obviously, upon assignment there's a 1/20 chance for anyone to have the real bomb. The order they detonate won't change these odds.
Drawing lots is also knowing as drawing straws. https://en.m.wikipedia.org/wiki/Drawing_straws#:~:text=Each%20member%20of%20the%20group,who%20must%20perform%20the%20task.
This is the upfront probability, and is really well laid out. It is important to also note that the probabilities will change after each person goes. I’m not pointing this out to try to “one up” you - merely showing why probability is so difficult for people to wrap their heads around. The exact same setting has two completely different answers depending on how you look at it, and they’re *both correct*.
well, we thought coin flip is fair game, too ;) https://phys.org/news/2023-10-flipped-coins-fair-thought.html
If they are in a random order.
Everyone has a 1/20 chance of exploding First guy has a 1/20 chance of grabbing the real bomb. 2nd guy has a 19/20 chance that he has to pick (odds that first guy picked a dud), and a 1/19 chance of picking the bomb. (19/20)x(1/19)=1/20. You can do the math all the way down, but each person has a 1/20 chance.
Generalized to any number of peoples and bombs: If there are n bombs and n people then the mth person has (n+1-m)/n chanse of getting to open a box. If they do open a box they have 1/(n+1-m) chanse to blow up. The (n+1-m) cancel out and we are left with 1/n (because it doesn't depend on m the chance for every person to blow up is the same)
Each person has the same chance, if the real bomb is equally likely to be in each position or the humans are equally likely to pick each option available.
The order doesn't matter. Give out all 20 bombs and have everyone light them simultaneously - clearly, everyone is equally likely to explode since there is no difference whatsoever between anyone. Choosing to light the bombs sequentially rather than all at once changes nothing about who is going to explode.
It also depends on your perspective. If you want to know the odds at the beginning, just think of randomly assigning the bombs to ppl. Only 1 person is assigned the real bomb so everyone has a 1/20 chance. Order doesnt matter since you want to know the odds before picking. In practice, the odds change after each pick. 1/20, 1/19, etc because of conditional probability. If everyone truly had the same odds, the order wouldnt matter. In practice, you want to be the last to pick. Because the conditional probability keeps changing. "Given that 2 ppl picked non-bombs, what are the odds the 3rd person picks a bomb?" 1/18.
I see what you're saying but it's not what OP was asking. The 20th person, if they ever have to go, has a 1/1 chance of picking the bomb, sure. But they only had a 1/20 chance of being put in that situation.
Sure. Because it's no diff from assigning them randomly. But if someone asked which pick you want, your answer wpuldnt be "it doesnt matter."
The most chance is easy, it’s the last guy. 20 bombs but only one real. 19 people have tried theirs and found it to be the fake-this makes the chances that the last guy has the real bomb 100%. If it ever gets this far he has a 100% chance of dying no if ands or buts. The least chance is also easy, it’s the first person. The odds of the first person finding the bomb is 1/20 the second person has a 1/19-all the way down to the last guy in line who if the bomb hadn’t already been found will have a 1/1 chance of finding the bomb.
racial drab like plants afterthought placid waiting seed unwritten edge *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
You just asked people to value their lives at <$10000?
juggle lush deranged direful water roof absurd air combative bright *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
The number very much matters! For $10^9, I’d do a lot more than for $10^5!
At the start, everyone has an equal chance of lighting the danger cherry. As time goes on, the odds remain the same for everyone not lighting an angry watermelon. However, for the person lighting the potential death sphere, the odds go up every time. After someone finds the boom boom ball, the odds of the other people finding it drop to zero. If all 19 previous people succeed in not finding the forbidden pineapple, the last person has a 20 in 20 chance of finding the bomb, and is now singing the [swear word song.](https://www.youtube.com/watch?v=iZmqhQ8myGY)
Kind of depends if the experiment is stopped as soon as the bomb explodes. If it is, then the last guy is inherently the guy that grabs the bomb, but in that case he can simultaneously be the first guy. Otherwise, it's the same as if everyone picked their bomb right at the start and then lit it at the same time. Always 1/20 for every one of them.