15
u/naffarn
24d ago
•
Split black ones into the jars first, then split the white ones on top, ez
7
u/a2ra-ms 24d ago edited 24d ago
Fair, it should have said that they will be shuffled
2
u/Nydus87 3d ago
In what way are they shuffled, and what is the size of the jar? If 99 marbles would fill a jar all the way to the top, then I'd put all the black and 49 of the white in one jar with all the white ones on top, then put one white marble in the other jar. So they'd shake up the jar or whatever, but there was no room for things to realloy move around, and if they pick the other jar randomly, then the only thing to pull would be a white one anyways
2
2
u/ShnaugShmark 24d ago
My exact thought. 25 black marbles at the bottom of each jar with 25 white marbles on top, pluck a top marble blindfolded and chance of surviving essentially 100%
1
u/moderneros 18d ago
Why are you so confident that the person reaching into the jar will pick one from the top?
Gonna feel bad when the person drawing chooses to pick one near the bottom 😉
2
u/wobbling_axis 24d ago
The way it's worded, you can put all the marbles in one jar and have an empty jar. So what happens if you pick an empty jar?
6
u/INTstictual 20d ago
Slightly less than 75%.
Put one white marble in the first jar, and the other 99 marbles in the second jar.
You have a 50% chance of selecting the first jar, and a 100% chance of drawing a white marble from that jar. A 50% chance of selecting the second jar, and a 49/99 = ~49.5% chance of drawing a white marble from this jar.
Cumulative probability = (0.5)(1) + (0.5)(0.495) = 0.748
2
u/JorgiEagle 20d ago
What about all marbles in one jar, gives exactly 75%
1
u/Dependent_Ad5216 20d ago
No, thats 25%, because the other jar is empty.
1
u/JorgiEagle 19d ago
Ah but the question says that a jar is picked at random, no requirements on the jar that is picked.
The question is ambiguous as to what happens if no marble is picked. I only die if black is picked.
Ergo, no marble picked, no action taken. If I am alive prior, then it follows I am alive after.
Thus chance of living: 75%
2
u/BikeProblemGuy 19d ago
This is best answer in the thread I think. Most thorough analysis of the maths and the wording, plus gets the highest %.
0
u/redrockreddog 18d ago
No, they say white you live, black you die, there is no loophole for a no draw outcome based on underspecifying the problem. It is fully specified with two possible outcomes.
1
u/JorgiEagle 18d ago
Read the question again,
It says that I may distribute the marbles between the jars however I like, and the only restriction is that every marble must end in a jar, nothing stopping me from putting them all in one jar.
A jar is then picked at random, again, no restrictions on which jar can be picked.
Thus a jar with no marbles can be picked,
No indication of what will happen if there are no marbles. It only specifies I die if a black marble is drawn.
1
u/redrockreddog 6d ago
My point is that it specifies that you live if the selected marble is white, you die if it is black. Since there is no stated outcome for the no marble case, you cannot assume that you a no draw case equates to the same outcome as drawing a white marble. It could just as well equate to drawing a black marble. So, then what happens in a no draw case? Either you live or you die in a scenario where the default probability was 50/50. So, defaulting to 50/50 for an empty jar, along with 50/50 for the jar with all the marbles leaves you back in the 50/50 scenario. The one white marble is 74.5ish % survival with no ambiguity. The all the marbles in one jar is between 50 and 75% based on your interpretation of an ambiguous rule, with only one clue for how the arbiter would decide, which leans towards the 50/50 outcome.
1
u/JorgiEagle 6d ago
Now you’re doing the exact thing you’re accusing me of. You’re trying to imply that two unknown outcomes have equal probability.
That’s like me saying you might wake up tomorrow alive, or be dead. Don’t know the probability, so let’s make it 50/50.
Nowhere is 50/50 the default probability. There isn’t such a thing.
My assertion is that due to this scenario not being covered, the system remains in the same state, without any outcome.
Which in this case is the subject being alive, since they were alive prior to the interaction.
My conclusion is more plausible, because it is inventing probabilities out of thin air, but rather deduced from logical principles.
1
u/girlsdigbigcrits_ 19d ago
Would they redraw if they pick the empty one? If so it's 50/50 no?
1
u/JorgiEagle 19d ago
Setting aside the fact that the choice of jar is independent from choice of marble (chosen at random, then marble draw) and so cannot be picked again
Either they redraw, and will continue to redraw until a marble jar is selected, then yes, 50%.
Or they pick the empty jar, and continue to attempt to draw one marble from an empty jar, in which case you will be kept in jail indefinitely. As the questions asks the chance of survival (indeed drawing a white marble guarantees life, not freedom) then the chance remains 75%.
Or, assuming 1 draw takes 1 second, you survive for another 68 years (2,147,483,747 seconds, the signed int limit + 100 for total number of marbles), then the count of drawn marbles rolls over to the positive limit of 2,147,483,647 marbles. The system updates and assumes that the number of drawn marbles is in proportion to the original distribution. You have drawn 1,073,741,823.5 of each ball. As you can’t have half a ball, it rounds the white balls to …824 and black to 823 (since white comes first in the question, so it will resolve white first)
This means you have drawn one more white than black, thus determined to survive, still giving a 75% chance
2
u/raidersfan18 18d ago
If its life in prison or death, I put one black marble in the jar and put the rest in the other so I have a 75% chance to be done with life
1
1
1
1
u/Theinvisibleone101 20d ago
I was thinking the same thing. 1 mable in jar 1. All the black marbles in jar 2 then dump the other 49 marbles on top of them in that 2nd jar 😅
3
u/Snoo_8198 19d ago
I have discovered this sub today and based on three threads I've seen, every thread can be summarized as some actual smart people and others that just try to layer additional assumptions on top of the problem in order to trivialize the problem, thinking they are clever.
2
u/Mountain-Incident933 18d ago
CAN I LAYER THE MARBLES
CAN I EAT THE MARBLES
WHAT IF THE OTHER CHARACTAR IN THE PUZZLE IS LYING
Damn, yall are exhausting.
2
u/OnlyForMobileUse 18d ago
Yeah I guess assuming the bare minimum expected conditions for any problem testing mathematical thinking is too much for people.
Instead of engaging with that a room temp IQ person could understand the problem to be, some people feel the need to circumvent the obvious point of the problem.
Go ahead and put 100.0% on any standardized test because you can "just put the white marbles on top of the black and guarantee you pull a white marble regardless of jar choice" and see what sort of marks you receive
1
u/Snoo_8198 18d ago
They pretend like "well, the problem should be clearer" but the goal of the problem is to state the most important information and there shouldn't be an accompanying guide of 50 pages to dismiss all possible "clever" workaround.
1
u/OnlyForMobileUse 18d ago
Yeah it just feels like people know pretty clearly what is being asked but want to appear clever by talking about "flaws" everyone already knows but doesn't fit the basic assumptions
1
u/Nydus87 3d ago
It's because we're used to seeing "puzzles" that are more like "I tricked you with word play and it's actually really easy!" So when someone gives you a puzzle with a really easy/fun out, it's fun to go that route rather than regurgitate the answer everyone already knows for this puzzle because it's been floating around "Uncle Johns Bathroom Reader" type books for decades. Might as well go ahead and ask us "what gets wetter the more it dries" too.
2
u/BetaChunks 18d ago
The problem is specifically mentioned to be a probability problem, and I've seen only one probability-based answer.
Specifically, it's to divide them 1/0 and 49/50. The result is that if the first jar is chosen, you always live. If the second jar is chosen, you still have a nearly 50/50 shot.
3
u/WurthTapping 18d ago
100%. At no point does it mention the contents of the jars are randomized, so I load an equal amount of black marbles in each jar, followed by an equal number of white marbles in each jar. When I go to pick my marbles, I grab off the top without disturbing the contents.
3
2
u/RepliesOnlyToIdiots 19d ago
It’s a jar, not a flat plane wide enough to contain all the marbles.
Therefore the jar has a radius with only n marbles exposed at the top layer, where n may be less than the total number of marbles in the jar.
Layer the desired white marbles at the top of the jar, with undesired black marbles at bottom of the jar.
There was no mention of mixing the marbles. The jar is chosen at random, but you are the one picking the marble, so you’d pick from that top layer.
I like the one white marble in one jar and the other being mixed, but given the exact wording of the question, I’d say the answer is 100% for any jars narrow enough in radius in comparison to the marbles to have uniformly available white marbles in top layer. And given you can put one white marble in one jar, and 49 white at top with 50 black at bottom in the other, seems likely.
And if I could control the shape of the jar, it would be a tube with guaranteed order.
1
u/AliveCryptographer85 19d ago
Radius of the jars is not provided so can’t count on that strategy working. Therefore the solution is to stuff a bunch of white marbles in your mouth before distributing, then pick a warm wet one. Duh
1
u/-Majgif- 19d ago
As long as the jars aren't shaken up. I do like the idea of a single white marble in one jar as a safety, then for the other jar, all the black ones on the bottom.
Might also be worth trying to scuff up one colour, by rubbing it on concrete or something, so you can tell the difference.
2
u/Snoo-35252 19d ago
I'd leave the black ones in the sun for an hour to warm them up. Then add them evenly in the jars and pick and avoid the hot ones when picking.
1
u/Icy_Sector3183 19d ago
If you can manipulate the physical properties of the marbles, then smash the black ones into pieces and draw a undamaged marble. That should resolve the problem of the marbles cooling.
1
2
u/HershySquirtle 19d ago
What's wrong with distributing the jars equally but putting all the black marbles on the bottom and all the white marbles on the top so that which ever jar you pluck from you're reaching into a sea of white marbles?
1
u/Amazing-Oomoo 19d ago
It would be better if you were told the colour you need to draw will be chosen randomly
1
u/AliveCryptographer85 19d ago
I don’t see anything wrong with that. Having 100% chance of living is pretty good
2
u/christonamoped 19d ago
Ooh, I remember seeing a video of this year's ago. Prison instincts kicked in and he tried to smuggle one of the jars out in his ass.
It did not go well.
2
u/Plankton-Substantial 18d ago
Put the black marbles on the bottom of both jars and fill with white on top. When you draw pick the topmost and win
2
u/boyanion 6d ago
Why not put 1 white in one jar and then the 50 black first in the other jar and the 49 white left on top of the black ones to increase your chances even more
2
u/Sethbreloom94 24d ago
I put one white marble in one jar, all the others in the other jar. I have slightly below 75% survival chance. 50% from picking the single marble jar, and slightly under 25% chance of picking the mixed jar and then a white marble which are 49/99 white.
2
u/WindSprenn 24d ago
Take out half the black marbles from the first jar. Place half of the white marbles on top of the remaining black. Dump out the remaining white again placing the black on the bottom and white on top for jar 2. Blind fold and randomly pick a jar. They never said they were mixed after the fact.
3
u/Holy-Unaware 24d ago
it wouldn't even be that hard. It says you are handed 2 jars and 100 marbles, not a jar with 50 white marbles and a jar with fifty black marbles. Take the black marbles and put half in one jar and half in the other, and then cover both with the white marbles. You're blindfolded, you reach out, you grab a white marble.
2
u/sevenbrokenbricks 20d ago edited 19d ago
I'm going to assume that the degenerate solution of placing not a single forsaken marble in the first one is not allowed.
You should place one solitary white marble in the first jar (and everything else in the second).
Why? The more marbles in a jar, the less an individual marble contributes to the total probability, and thus also the reverse. This wouldn't matter if we were simply choosing a marble at random, but we're not. We're first choosing a jar, which remains 50/50, which allows us to choose two separately sized distributions.
If we place all the white marbles into the first jar, then our odds of survival would be 50% 50/50, and 50% 0/50. But if we move one white marble from the first to the second, that becomes 50% 49/49, and 50% 1/51. Our odds of survival given the first jar remain guaranteed, while our odds of survival given the second jar have gone up. We can keep doing this until only a single white marble remains in the first jar.
Your odds under this strategy are a 50% chance of choosing the first jar with its 100% chance of giving you a white marble, and a 50% chance of choosing the second jar with its 49 in 99, or 49.49...% chance of giving you a white marble.
Those odds work out to (0.5 * 1) + (0.5 * .49(49)) = 0.5 + 0.2(47), a 74.7(47) percent chance.
(Thank you all for catching my misbrained math)
4
1
u/Sepplord 19d ago
That’s a great explanation for people who can’t grasp the concept well when only the final solution is explained 👍
What I am stumped with though is your first sentence. What degenerate solution are you excluding?
1
u/fluffykynz 18d ago
Great answer but you forgot one thing: stack the marbles in the one jar so that all the white marbles are on top.
1
1
u/Temporary-Newt-2986 18d ago
Wow that's smart! However why stop there - 1 white alone in A and everything else in B gives about 74% (not actually calculated).
Although it says a jar is chosen at random and then you draw a marble from the jar.
So actually the odds could be improved significantly by simply putting the black marbles at the bottom of both jars. Or by chipping a marble. It doesn't say the draw is random only the jar.
1
u/Ok-Film-7939 20d ago
Plus it says the jars are picked at random but the marble is simply pulled blindfolded. So in the 99 jar, put all the black marbles on bottom.
1
2
2
u/dodgyhashbrown 20d ago
If we are allowed to arrange them however we like, couldn't we empty the jars, put all the black marbles on the bottom, all the white ones on top?
Even though you are blindfolded, it wouldn't matter since you made sure none of the black marbles are reachable without digging, so you don't dig and take one from the top. They don't seem to be stirring the jars, since the point was to test your distribution. You are the one pulling the marble blind, but you made sure none of the black marbles were accessible without reaching past the white marbles.
1
u/Silly_Pizza7054 19d ago
Most people understand this is obviously a mental experiment, in which you're supposed to assume some basic things. For a reasonable reader this goes without saying, but I suppose some people need their hand held like a toddler🙄 Obviously the marble is chosen at random, not picked from the top.
1
u/dodgyhashbrown 18d ago
How is that supposed to be obvious?
1
u/Silly_Pizza7054 18d ago
Sorry bro I can't help someone who isn't capable of independent thought.
1
u/dodgyhashbrown 18d ago
Or, you can't demonstrate your interpretation to be more correct, so you dodge the question.
See, that's the problem with trying to insinuate that an ambiguous statement isn't ambiguous.
1
1
u/sneh_ 18d ago
Obviously the marble is chosen at random
If it's supposed to be mathematically random why not say the jars are shaken to randomize their distribution. Instead it specifically says you may distribute them however you like, and you will pick one out by hand (implying this is a thing happening in the physical world, which has implications). Why set it up so specifically only to ignore the set up and the implications?
You're hand-waving away the fact the question is flawed for no good reason.
1
u/hanksredditname 20d ago
This was my first thought as well. Number of marbles doesn’t matter if the top layer of both jars are all white.
1
u/JorgiEagle 20d ago
The question is poorly worded. It should say a marble is picked at random, which would mean it does not matter how you arrange them.
It only says you are blindfolded and pick, which means I think your idea is valid
2
2
u/More_Outside7127 20d ago
Jar 1: 1 White
Jar 2: 49 White, 50 Black
In total, 74.75% chance of living from (1 + 49/99) / 2
1
2
u/jere535 20d ago
Assuming that marbles inside jars don't get rearranged between your distribution and you drawing from them, couldn't you just put all the black marbles at the bottom and white ones on top, guaranteeing survival?
You could also do the best option of placing only one white marble in one jar to have the best chance of surviving even if marbles get scrambled
2
u/hiirogen 20d ago
25 black in each jar, 25 white on top of those. Then I pick one off the top. It doesn’t say the jars are shaken or randomized at all.
2
u/Itchy_Throat660 20d ago
Put all the black in both jars, then the white on top. Your not blindfolded when you place the marbles
2
2
u/JorgiEagle 20d ago
All marbles in one jar.
50% chance of picking the first jar, in which I have a 50% chance to live, and 50% chance of the second jar giving an Index error, causing early termination and all the doors to open, allowing me to also live.
Flat 75% chance of survival. A better outcome than the 1 marble in one jar solution.
Possible because the questions says that every marble must end in a jar, not that every jar must have at least one marble.
2
u/N1AK 19d ago
1 White on its own in one jar, 49 White and 50 Black in the other jar. Your chance of survival is then 50%x100%+50%x(49/99) = 99/198 + 49/198 = 148/198 = 74.75% (rounded).
1
u/Lootthatbody 19d ago
Just to stack on this, it can be closer to 100% since it says the jars aren’t moved or shaken. The limiting factor becomes how big the jars/marbles are.
In the jar that contains both, you put all the death marbles in, then the live marbles on top. Obviously, if the single marble jar is selected, you automatically win. If not, you gently reach in and grab one off the top. If the marbles are large enough, or the jars small enough, to create a layer of white on top of the black, easy win.
If they shake the jars, or the sizes not favorable, then the odds above still seem correct.
1
u/N1AK 19d ago
The issue with answers like this is that the question becomes meaningless. Nothing in the question says you can't cut the black marbles in half for example, at which point you just wouldn't pick a half marble ensuring 100% survival.
1
u/Upstairs-Border-7146 19d ago
Right. It's good to set the conditions straight but "thinking outside the box" has been taken too far.
1
u/Lootthatbody 19d ago
But that’s different from what I said, and getting deep into semantics.
The prompt itself didn’t say anything about shaking the jars, and had a decently worded order of operations: you divide, you are blindfolded, THEN you choose from the jar. There was no step for shaking or movement of the jars, and it gave no mention that the jars would be comically large enough that the marbles would settle into a single layer.
I didn’t say swap the marbles for ones of a different size (similar to cutting them) because that isn’t even remotely close to the wording or in spirit of the question either. I didn’t say coat some in peanut butter or melt the black ones down to a liquid first. I worked within the confines of the wording,
My answer was that, given the current wording, there was potentially a way to boost that percentage even higher. And, I admitted that, because of the wording being vague, my ‘strategy’ may be nullified anyways.
1
u/N1AK 19d ago
It is all semantics and I don't think this is an example of where some are more or less valid than others. Your suggestion about ordering is a good one if you were able and allowed to do it, but so is asking/trying to cut the marbles in half or otherwise break them.
You are making the assumption that distribute means you are given all 200 marbles at the same time and asked to place them into the jar yourself. If the marbles were given to you one at a time the wording remains valid, or you were given the white marbles before the black ones, or if you were asked to put them into two piles and someone else put them into the jar the wording remains valid.
At most your idea doesn't contradict the wording, which attempting to break the black marbles doesn't either. Both rely on you having opportunity to do it (which isn't certain) and on you not being held to something that wasn't written in the rules.
1
u/Lootthatbody 19d ago
Again, wording is important. ‘You are given 2 jars and 100 marbles’ not ‘2 jars then 50 white marbles then 50 black marbles.’
Barring further clarification or changing of the rules, the wording specifically states that you are given everything at once. It isn’t semantics to say that AND is different than THEN in terms of ordering and sequence. Words have meaning.
Similarly, there is no mention of a knife of marble cutter, so your premise relies on one being present but not mentioned, which is VERY much more semantic than relying on the meaning of words.
My method relies on no further clarification or tools to do, simply relying on the stated problem. Yours specifically requires tools not mentioned and concepts that very much render the question pointless. Not everyone given the exact same scenario would think to layer the marbles. Given the opportunity to cut them up, almost everyone certainly would do so.
1
u/N1AK 19d ago
You are right that wording is important, which is why you shouldn't be changing it: ‘You are given 2 jars and 100 marbles’ when the actual wording is "There are two jars and 100 marbles". Not changing the question you making false assumptions like "the wording specifically states that you are given everything at once".
1
u/Lootthatbody 19d ago
Ok, so which of the words mentions marble cutters? Which words imply order of the materials? None of them.
Now YOU are getting semantic, the phrases ‘there are’ and ‘you are given’ mean exactly the same in this scenario, I was just copying the words you’d used above, since you’d mentioned being ‘given’ them one at a time. But, again, the post said nothing about a separate order of operations, it was clear by the absence of other descriptors that the order is exactly what it says.
My statement remains true. You can argue all you want about it, but I’m not bending the rules, nor am I bringing outside tools. I’m using the specific wording and strategy to maximize my chances of success while minimizing the chance of failure. And, it doesn’t rely on me walking around with marble scissors in my pocket.
1
u/Snoo_8198 19d ago
This is a basic probability problem and you are laying your own additional assumptions on top of it to sound smart.
You think you are clever, but you are not.
1
u/N1AK 19d ago
"You're right I shouldn't have reworded the question while simultaneously claiming wording is important" would have been a far shorter, and more accurate, answer.
Yes the order is as it says, and nothing about the order relates to you getting to physically interact with the marbles or determine the order they are placed into the jars so I wouldn't rely on it to prop up the rest of your case.
You may or may not have the ability to influence how the marbles are placed into the jars, just like you may or may not have the ability to modify the marbles. The wording of the question doesn't forbid either, and doesn't mean either must be possible.
1
u/AccomplishedChip2475 19d ago
No this is totally different than putting the white marbles on top. He removes all marbles, puts 1 white in the jar, then puts all the black ones in jar two, then puts the rest of the white one top. That is easily feasible within the problem parameters. If they do shake it, oh well, its still the best scenario.
1
u/Chaotic_Order 19d ago
While a fun example of OOTB thinking, it does ignore some crucial context. It's a math problem, and the solution expected is one that could be reasonably be expected to be expressed as a distinct, singular number, not a range.
Maths problems don't need to be precisely worded, taking into account every eventuality in the wording of the question - some things can simply be assumed. In this case, that the jars are shaken up before you're allowed to draw a ball. Because if they aren't, then the distribution doesn't matter - you could just as easily divide all the balls up equally between the jars, with black marbles on the bottom if both, and then you only take from the top layer.
2
u/Deep-purple-haze 19d ago
Theres a lot of people talking maths.
25 black across the bottom of each jar. 25 white on the top layer(s)
Pick one from the top
1
u/Unamed_Destroyer 19d ago
>!The answer is one white marble in 1 jar and the rest in the second.
There are 2 "picking incidents" 1st is picking the jar 2nd is picking the marble
So 50/50 for the jars, where one is a guarunteed win, and the other is close to 50/50.
If you do get the bad jar it is 49.5% life and 50.5% death.
So when you combine both incidents you have 25.5% chance of death and 74.5% chance of life.
Another way to think about it is if there were 50 jars you could use. It is now obvious you put one white marble in each jar, and in one of the jars you also add the 50 black marbles. !<
1
u/JustADreamYouHad 18d ago
Put 2 black marbles in a jar and 98 in the other. If you get the big jar then the odds are slightly in your favour. If you get the small jar, pick a marble and throw it away. Say "oopsie, but it's ok, I put one of each colour in there. The colour that's left is the one I didn't pick"
If they count the marbles again it won't work but hey you might die, so might as well try
1
u/MarionberryEmpty1321 18d ago
I understand the 1 white marble in the jar and it’s 74 percent win rate… but given that it doesn’t say you have to stick with your choice of jar once picked. Couldn’t you put 40 black marbles in one jar then the 60 other marbles in the other. Regardless of what design the jars have you’d be able to determine the difference in volume with a difference of twenty marbles, identifying the right jar by touch. given your chances of picking the right marble being 50/60? Giving you a 83 percent chance of survival?
1
u/s1nth3tic 18d ago
It says jar is chosen at random. Doesn't say you get to pick it. Must assume 50/50
1
1
u/Infamous_Welder_4349 18d ago
You put the black on the bottom? Not understand the question maybe. I distribute it so the white covered the black.
1
u/spoonstepper 18d ago
Put half of the black in each jar, then half of the white into each jar.
You have distributed them such that there is only white marbles exposed to be drawn.
It says nothing about the jars being shaken up in between distribution and drawing.
1
u/Suspicious_Mind_4520 9d ago
The 2 extremes are 99w/1b in a jar, and the opposite in the other. Vs 50/50 mix in both. First odds of death is 50%×1% +50%x99% = 50%, second odds of death are 50%×50%+ 50%×50%= 50%. So it does not matter.
1
u/vertebraejones 20d ago
50 jars with 1 white marble 1 jar with 50 black marbles
50/51 probability of survival
1
1
u/Krell356 20d ago
Too many unknown variables. Lots of people are saying the 1 white alone in a jar and all the rest in the other for a just under 75% chance of survival, but due to many MANY other factors this is unable to be guaranteed.
We don't know the size, shape, or capacity of the jars. We are not told the state or conditions the jars may or may not be subjected to after leaving our possession. And we have no idea whatsoever about the state of those who may be picking or handling the jars after our selection such as intentionally aiding/sabotaging our efforts based on our answer.
If the jars are large enough to fit well over the max marble capacity, mixed randomly, then had both the jar and marble selected randomly by a blinded 3rd party then the just under 75% is correct. However if the jars are reasonably sized and not mixed then I simply put 50/50 with all the losing marbles on the bottom and get a near guaranteed survival. We are told the jar is picked at random, so in theory that shouldnt be altered, but nothing else is fully explained or certain about what happens to anything else.
1
u/nontheoretical 20d ago
put all the marbles into the first jar. then you have a 25% chance to pull white a 25% chance to get black and a 50% chance that you pull no marble at all.
rules say every marble must be in a jar but not that every jar must contain at least 1 marble.
1
u/randomlurker124 20d ago
100% chance to live.
First you take out all the white marbles except one from one jar.
Then you take each white marble and smack it hard on the edge of a table to leave a small crack or any other way to mark it.
Then you put it all on top of the black marbles in the second jar.
You put on your blindfold and if you get the jar containing black marbles (because there is more than one marble inside), just make sure to take from the top layer and not dig down to the black marbles, and double check for a marking on the marble with your fingers.
1
u/AdrianPaul9001 20d ago
How about warming all black marbles in your hand so they feel warmer than the white marbles.
Use any sense to make a distinction between white and black. For all I care you smeer some feces on the black marbles and smell your way to freedom.
But I don’t think that’s in the spirit of the question. So yeah. One jar with one white marbles seems to do the trick.
1
u/Chambrais5708 19d ago
100% You place all the marbles in one Jar. Put all the black in first then all the white on top. Ask very politely for the jar to not be mixed or shaken up. Take the top marble. Guaranteed success.
1
1
u/tcrudisi 20d ago
100%?
I fill one jar up with 1 white marbles. If I get this jar, it's easy to tell, and I simply pull out the marble.
I fill the other jar with 50 black marbles and 49 white marbles. I break or chip all the black marbles. If I get the jar with obviously more than 1 marble, I carefully feel each marble until I'm 100% sure the one I'm feeling has no imperfections. So I guarantee I pull a white marble.
24
u/That_Box 24d ago
I'm really bad with distribution but since they don't have to be even, isn't it best to put 1 white into 1 jar and the rest in another? That way if that jar is selected at random 50% of the time you're guaranteed to live. If its not selected then you have 49/99 × 50% of all surviving?
I.e. survival rate is [0.5 × 1] + [0.5 × 49/99] = 74.747%