Brain Teasers
Losing Your Marbles
Fun: (2.23)
Difficulty: (1.11)
Puzzle ID: #39231
Submitted By: tricky77puzzle Corrected By: tricky77puzzle
Submitted By: tricky77puzzle Corrected By: tricky77puzzle
Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability
There are 3000 marbles in a machine - 1000 red, 1000 green, and 1000 blue. The machine churns out a random number of marbles into a bag (any number from 1 to 3000), without letting you see the inside, so you don't know how many of each colour, or in total, there are. What is the probability, without looking into the bag, that you will pick out a red marble?
Hint
The bag is only an intermediary step... The answer is the same even when weighing out all the cases, because you don't know what marbles the machine churned out.Answer
The probability is 1/3. The bag is an intermediary step intended to mislead you into thinking it's something else.Even if the machine does churn out only blue and green marbles and the probability directly from the bag is 0%, you don't know that, and it could have picked out only red marbles, in which case the probability is 100%. All the cases average out to 1/3.
The probability is the same as if you picked one directly from the machine.
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Great teaser! You had me for a minute, but on second thought the answer was plain!
The question asks what is the probability of pulling a red marble out of the bag, yet the answer states the bag is unimportant as the pobablity id based on the content of the machine? Surely if for example the machine dispenses 6 marbles, 3 blue and 3 green, then the probability of drawing a red from the bag, as asked in the question, can not possibly be 1:3 as there are only two possibly outcomes and neither include the possiblity of drawing a red. The overall probability if you repeat the experiment numerous time is 1:3, but with just one random delivery of marbles into the bag, as stated in the question, the probability is not 1:3. You can't ask " What is the probability, without looking into the bag, that you will pick out a red marble?" and then in the answer say the contents of the bag is irrelevant. If only two colours are in the bag, then the possiblity of pulling another colour is 0.
Thought it was great keep making them
It was good
To Mad-Ade: A lot of people have trouble with this explanation.
However, your saying that the experimental probability is the true probability is correct. The theoretical probability in each different case is of course different, but since you don't know what case is taken into consideration, you need to take all the cases into consideration, and this makes the bag irrelevant to the solution.
However, your saying that the experimental probability is the true probability is correct. The theoretical probability in each different case is of course different, but since you don't know what case is taken into consideration, you need to take all the cases into consideration, and this makes the bag irrelevant to the solution.
The probability of the machine despensing a red is 1:3, the probability of drawing a red from the bag relies on the number of different colours with in the bag to begin with, If you are to empty the machine in varying stages into the bag and record the overall result, it would be 1:3. If there is only one such dispensment in to the bag which deposits, for example, only blue and green marbles in the bag then the probability of drawing a red one is none existant. As I said previously, your question asks for th probability of drawing a red from the BAG, your answer gives the probability of drawing from the over all contents of the machine.
Well then, if it were truly to be the actual probability drawn from the bag, then the answer would be different every time!
(Anyway, let's stop arguing.)
(Anyway, let's stop arguing.)
The overall probability if ALL the balls were eventually drawn from the bag would indeed be 1:3, but that is not the question asked, as it is every single draw could have a different probability based on which marbles are actually available to draw from with in the bag, obviously if no red marbles present then the probability of drawing one is not 1:3 as there are only two colours to choose from so a probability ratio of 0:2 would be more accurate for that instance, where as if the are all red balls, the ratio would be 1:1. So just one random amount of balls in the bag would not give a 1:3 ratio unless it was know that all three colours were present.
Made-Ade, the question doesn't ask what is the probability of picking a red marble out of the bag but what is the probability of picking out a red marble.
This is an experiment that has two steps: 1) a random number of balls (of random colour) go into a bag, and 2) a random ball is selected from the bag. There is no reason to assume that the question only wants to know the probablity of the second step (which both you and the quiz creator pointed out has a variable probability and can range from 0% to 100%). Because we know all possible outcomes of step 1 we can work out all possible outcomes of step 2. There are many, many more outcomes in this experiment than there would be if you just selected a ball from the machine, however one third of these are still the event "you pick out a red marble". Saying this answer is different is like saying there is a difference between 2/5 and 40/100.
If you feel like disagreeing with what I said don't bother. You can argue all you like that the question was asking for the probability of the second step but I understood it to mean the experiment on the whole and I'm assuming most other people that read it would too.
By the way, 1:3 is not 1 in 3 it means 1 to 3, if there is 1 red and 2 other colours then that is 1:2 (1 to 2) or 1/3 (1 in 3).
This is an experiment that has two steps: 1) a random number of balls (of random colour) go into a bag, and 2) a random ball is selected from the bag. There is no reason to assume that the question only wants to know the probablity of the second step (which both you and the quiz creator pointed out has a variable probability and can range from 0% to 100%). Because we know all possible outcomes of step 1 we can work out all possible outcomes of step 2. There are many, many more outcomes in this experiment than there would be if you just selected a ball from the machine, however one third of these are still the event "you pick out a red marble". Saying this answer is different is like saying there is a difference between 2/5 and 40/100.
If you feel like disagreeing with what I said don't bother. You can argue all you like that the question was asking for the probability of the second step but I understood it to mean the experiment on the whole and I'm assuming most other people that read it would too.
By the way, 1:3 is not 1 in 3 it means 1 to 3, if there is 1 red and 2 other colours then that is 1:2 (1 to 2) or 1/3 (1 in 3).
Also, if you have all red balls and no other colours then the ratio is 1 (or 1/1) and not 1:1.
that should be 1 : 0 not 1
J-Me, the question DOES indeed ask about the probability of drawing a red marble out of the bag, obviously you missed the part where the teaser states "What is the probability, without looking into the bag, that you will pick out a red marble?" which is exactly the step two part of the responce you gave, the question is NOT asking what the over all probability is, but what the probability of one random draw from the bag, which is exactly the step two you mentioned. The answer on the other hand, says to IGNORE the bag, even though that was the principle and basis of the question. It is the phrasing of the question that is wrong, not the probability on the whole. You may wish to ASSUME that it is for the probability as a whole, and that is maybe what the writer meant it to be, but it is NOT the question asked. The question SPECIFICALLY asks for the probability on one random draw from the bag. I am not arguing, just pointing out that the answer does not answer the question asked.
Again, try to remember this is an activity (usually called an experiment in probability theory) that has a two-step process. The first step is from a known source of marbles (i.e. 1,000 red, 1,000 blue and 1,000 green) a group of marbles are placed into bag – this group has a random quantity of marbles that can range from 1 blue marbles and no others to 1000 marbles of each colour. The second, and also importantly final, step in the process is to select a single, random marble from the bag.
So, "What is the probability, without looking into the bag, that you will pick out a red marble?" just means that the quantities and colours of the marbles used in the second step are to remain unknown. Even if the final sentence read, "What is the probability of picking out a red marble from the bag?" it still wouldn't be asking for the probability of the second step, that is picking a marble out of a bag. This is because it's used in the question in the sense of the final step (e.g. "On completion of the final step what is chance of ending up with a red marble?"). You will note that I'm not arguing that the question implies just one draw from the bag – I agree with you on that point entirely. I am trying to highlight to you that picking a marble from the bag is merely the second and final step of a two-step process and that the question is asking for the probability of ending up with a red marble (in a single draw).
You can perform this activity a single time and you can determine the odds of getting a red marble at the end of the process – despite the fact that you cannot determine what marbles the red bag will contain. The reason for this is because while we do not know the outcome of the first step of the process we know every outcome that is possible from the first step. From there you can work out every single outcome for the second step from all the possible outcomes of the first step. This gives us every single possible outcome of the process and allows us to determine how likely the event "you pick out a red marble in the second step" is. Basically we can determine the probability matrix.
If this still isn't making any sense then think about all of the possibilities if there was only a single marble of each colour in the process. It still fits your objection, if in the first step of the process a blue marble, or a green marble, or a blue and a green marble went in the bag there'd be no possibility of picking a red marble from the bag in the second step of the process. If you think this will work because I'm using only a single marble of each colour then I suggest you do up a matrix having two marbles of each colour (and so on until you finally realise it's correct). Here's all the possibilities:
[Step 1 -> Step 2]
R -> R
G -> G
B -> B
RG -> R
RG -> G
RB -> R
RB -> B
BG -> B
BG -> G
RGB -> R
RGB -> G
RBG -> B
Those are the twelve possible outcomes of the activity. Knowing all of the outcomes means we can determine that at the end of the final step in the process there are four outcomes where the event is "you select a red marble." In other words without looking in the bag we know there's a one in three chance of getting a red marble. You may also note that when there's only one marble in the bag there is a 33% chance that you will have a 100% chance of selecting red, when there are two marbles you have a 66% chance that you will have a 50% chance of selecting red and when there are three marbles there is a 100% chance you will have a 33% chance of selecting red.
If that still hasn't sunk in then perhaps we should move away from marbles and bags and move onto something with even less possibilities: coins. If we flip a coin twice we know that there is a 50% chance that the results will be different. We know this without knowing the result of the first coin toss because we know all possible outcomes of two coin tosses, that is HH, HT, TH, & TT. If you are thinking about claiming that this is different, as we know that the second coin will be have a 50% of heads or tails on the second flip then I wish you'd start paying attention when I say to take note of something. We do know the odds of picking a red marble out of the bag, more accurately we know all of the different odds of picking a red marble out of the bag. Imagine having a random number generator that first generators either a 1 or a 2, if it generates a 1 it then generates another random number from 1 to 2 and displays it on the screen whereas if it generates a 2 on the first go it then generates a random number from 1 to 3 and then displays it on the screen. Just as you can work out the odds that you the random number generator will generate a 3 (despite it largely depending on the first number generated and not always being possible to generate on the second) you can work out the likelihood of picking a red marble.
If you don't understand this, that's a shame but I'm certainly not going to explain it to you again.
So, "What is the probability, without looking into the bag, that you will pick out a red marble?" just means that the quantities and colours of the marbles used in the second step are to remain unknown. Even if the final sentence read, "What is the probability of picking out a red marble from the bag?" it still wouldn't be asking for the probability of the second step, that is picking a marble out of a bag. This is because it's used in the question in the sense of the final step (e.g. "On completion of the final step what is chance of ending up with a red marble?"). You will note that I'm not arguing that the question implies just one draw from the bag – I agree with you on that point entirely. I am trying to highlight to you that picking a marble from the bag is merely the second and final step of a two-step process and that the question is asking for the probability of ending up with a red marble (in a single draw).
You can perform this activity a single time and you can determine the odds of getting a red marble at the end of the process – despite the fact that you cannot determine what marbles the red bag will contain. The reason for this is because while we do not know the outcome of the first step of the process we know every outcome that is possible from the first step. From there you can work out every single outcome for the second step from all the possible outcomes of the first step. This gives us every single possible outcome of the process and allows us to determine how likely the event "you pick out a red marble in the second step" is. Basically we can determine the probability matrix.
If this still isn't making any sense then think about all of the possibilities if there was only a single marble of each colour in the process. It still fits your objection, if in the first step of the process a blue marble, or a green marble, or a blue and a green marble went in the bag there'd be no possibility of picking a red marble from the bag in the second step of the process. If you think this will work because I'm using only a single marble of each colour then I suggest you do up a matrix having two marbles of each colour (and so on until you finally realise it's correct). Here's all the possibilities:
[Step 1 -> Step 2]
R -> R
G -> G
B -> B
RG -> R
RG -> G
RB -> R
RB -> B
BG -> B
BG -> G
RGB -> R
RGB -> G
RBG -> B
Those are the twelve possible outcomes of the activity. Knowing all of the outcomes means we can determine that at the end of the final step in the process there are four outcomes where the event is "you select a red marble." In other words without looking in the bag we know there's a one in three chance of getting a red marble. You may also note that when there's only one marble in the bag there is a 33% chance that you will have a 100% chance of selecting red, when there are two marbles you have a 66% chance that you will have a 50% chance of selecting red and when there are three marbles there is a 100% chance you will have a 33% chance of selecting red.
If that still hasn't sunk in then perhaps we should move away from marbles and bags and move onto something with even less possibilities: coins. If we flip a coin twice we know that there is a 50% chance that the results will be different. We know this without knowing the result of the first coin toss because we know all possible outcomes of two coin tosses, that is HH, HT, TH, & TT. If you are thinking about claiming that this is different, as we know that the second coin will be have a 50% of heads or tails on the second flip then I wish you'd start paying attention when I say to take note of something. We do know the odds of picking a red marble out of the bag, more accurately we know all of the different odds of picking a red marble out of the bag. Imagine having a random number generator that first generators either a 1 or a 2, if it generates a 1 it then generates another random number from 1 to 2 and displays it on the screen whereas if it generates a 2 on the first go it then generates a random number from 1 to 3 and then displays it on the screen. Just as you can work out the odds that you the random number generator will generate a 3 (despite it largely depending on the first number generated and not always being possible to generate on the second) you can work out the likelihood of picking a red marble.
If you don't understand this, that's a shame but I'm certainly not going to explain it to you again.
I think you are confusing the actual probability with the actual question asked. The question is "What is the probability, without looking into the bag that you will pick out a red marble?" anything before that become irrelevant. We are only looking at the probability of what can be drawn from the bag. It is not a two step anything; the question negates that by asking JUST for the probability of what is drawn from the bag ONLY.
Your last post is correct if you ignore the actual question asked.
I understand the points you are trying to make, but you fail to understand the question asked. It is NOT the overall probability but the ACTUAL probability of drawing a red marble out of a bag which may not even contain any red marbles. Your explanation, whilst correct, only gives an AVERAGE of ALL possible probabilities not that of the question asked.
If that is still not clear enough, imagine if I have three barrels of fruit, one containing apples, one with bananas and one oranges and you come to me and ask for three pieces of random fruit to be placed in a box and sealed for you to take home. If I put three bananas in the box, the probability of you pulling out an apple from the box when you get home is not 1:3. The probability of me putting an apple in the box is 1:3, but your probability pulling an apple from the box is dependant of what I actually put in it.
Your last post is correct if you ignore the actual question asked.
I understand the points you are trying to make, but you fail to understand the question asked. It is NOT the overall probability but the ACTUAL probability of drawing a red marble out of a bag which may not even contain any red marbles. Your explanation, whilst correct, only gives an AVERAGE of ALL possible probabilities not that of the question asked.
If that is still not clear enough, imagine if I have three barrels of fruit, one containing apples, one with bananas and one oranges and you come to me and ask for three pieces of random fruit to be placed in a box and sealed for you to take home. If I put three bananas in the box, the probability of you pulling out an apple from the box when you get home is not 1:3. The probability of me putting an apple in the box is 1:3, but your probability pulling an apple from the box is dependant of what I actually put in it.
omg if it got accepted it works lol
i got the answer though, and Mad-Abe (i think) I have to say that your wrong, being a *cough* registered *cough* mathmatician *cough*
i got the answer though, and Mad-Abe (i think) I have to say that your wrong, being a *cough* registered *cough* mathmatician *cough*
(SIDE A)
Hey Mad-Ade,
For a start 1:3 is a ratio that is the equivalent to 1 in 4 or 1/4.
Secondly, the only thing changed in your example is the fact that we don't know how many of each fruit we have. However, I'm fairly certain that because we know the ratio of apples to the rest of the fruit (i.e. 1:3 - or 1/4) the end probablity would be 1/4 (which is 1:3). I could be wrong but I can't be bothered checking it. Yet again, we don't need to know what's in the box, we just need to know everything the box could contain and everything that could come out of the box for every single possiblity of what the box could contain - there is no assumption that there is an apple in the box.
I already covered the context issue and why even if the question had been asked "what is the chance of pulling a red marble out of the bag?" it would have still meant for you to take into account the whole process and not just the second step. Yet again, is there any reason why we should assume the questioner wanted us the focus on the second step and not the whole process. If this was the case why wouldn't the questioner have asked, "What are all of the probabilites of taking a red marble out of the bag?" instead of "What is the chance of drawing a red marble out of the bag?" The fact that it asks for one probability and not for multiple probabilities is fairly strong evidence that it wants the answer for the whole process.
You keep harping on about how there could be no red marbles in the bag as if it's not taking into account then you fail to pay attention to the fact that it is taken into account, in fact you show a complete lack of understanding of the matrix when you say I averaged the results. No, the results were 12 total outcomes (note how sometimes the bag contained no red marbles), 4 events were "picking a red marble out of the bag". Have a look at the matrix again, there is absolutely no assumption that there is even a red marble in the bag. Read that sentence again just in case you brushed over it. There is absolutely no assumption that there is a red marble in the bag. The probability 1/3 doesn't come from assuming there is a red marble to pull out - it comes from looking at all possible outcomes, including the outcomes where there was no red ball in the bag and then arises at the probability of 1/3 (or more accurately 4/12 for my matrix). Having a 1 in 3 chance does not mean there has to be a red marble in the bag. Yet again, read that again: Having a 1 in 3 chance does not mean there has to be a red marble in the bag. That sounds counter-intuitive but it is because we are looking at the probability of the exercise (which is 2 steps remember) and not answering what are of the probabilities of the second step. The fact that the questioner asked for a single probability and not for multiple probabilities should have clued you in on that.
In a two step process if you know all of the possible outcomes of the second step for all of the possible outcomes of the first step then you can work out what the probability of an event at the second step has of occuring. If you know what happened on the first step (e.g. you look in the bag) those odds will change the probabilities of the events of the second event occuring (e.g. if you look in the bag and see there is no red marbles the probability of picking out a red marble would change from 1 in 3 to a 0% chance).
++PLEASE TURN OVER TO SIDE B++
Hey Mad-Ade,
For a start 1:3 is a ratio that is the equivalent to 1 in 4 or 1/4.
Secondly, the only thing changed in your example is the fact that we don't know how many of each fruit we have. However, I'm fairly certain that because we know the ratio of apples to the rest of the fruit (i.e. 1:3 - or 1/4) the end probablity would be 1/4 (which is 1:3). I could be wrong but I can't be bothered checking it. Yet again, we don't need to know what's in the box, we just need to know everything the box could contain and everything that could come out of the box for every single possiblity of what the box could contain - there is no assumption that there is an apple in the box.
I already covered the context issue and why even if the question had been asked "what is the chance of pulling a red marble out of the bag?" it would have still meant for you to take into account the whole process and not just the second step. Yet again, is there any reason why we should assume the questioner wanted us the focus on the second step and not the whole process. If this was the case why wouldn't the questioner have asked, "What are all of the probabilites of taking a red marble out of the bag?" instead of "What is the chance of drawing a red marble out of the bag?" The fact that it asks for one probability and not for multiple probabilities is fairly strong evidence that it wants the answer for the whole process.
You keep harping on about how there could be no red marbles in the bag as if it's not taking into account then you fail to pay attention to the fact that it is taken into account, in fact you show a complete lack of understanding of the matrix when you say I averaged the results. No, the results were 12 total outcomes (note how sometimes the bag contained no red marbles), 4 events were "picking a red marble out of the bag". Have a look at the matrix again, there is absolutely no assumption that there is even a red marble in the bag. Read that sentence again just in case you brushed over it. There is absolutely no assumption that there is a red marble in the bag. The probability 1/3 doesn't come from assuming there is a red marble to pull out - it comes from looking at all possible outcomes, including the outcomes where there was no red ball in the bag and then arises at the probability of 1/3 (or more accurately 4/12 for my matrix). Having a 1 in 3 chance does not mean there has to be a red marble in the bag. Yet again, read that again: Having a 1 in 3 chance does not mean there has to be a red marble in the bag. That sounds counter-intuitive but it is because we are looking at the probability of the exercise (which is 2 steps remember) and not answering what are of the probabilities of the second step. The fact that the questioner asked for a single probability and not for multiple probabilities should have clued you in on that.
In a two step process if you know all of the possible outcomes of the second step for all of the possible outcomes of the first step then you can work out what the probability of an event at the second step has of occuring. If you know what happened on the first step (e.g. you look in the bag) those odds will change the probabilities of the events of the second event occuring (e.g. if you look in the bag and see there is no red marbles the probability of picking out a red marble would change from 1 in 3 to a 0% chance).
++PLEASE TURN OVER TO SIDE B++
(SIDE B)
Here's the final final attempt:
PART A - let's have a story and say that the exercise (only involving 1 marble of each) is actually done by Bill. A machine churns out a random selection of marble and they are put into a bag, there is a green marble and a blue marble but no red marble in the bag. Bill is explained how the machine works and told how many marbles there are of each colour and asked to work out the possiblity of him picking out a red marble without looking in the bag. Bill realises that there may not be a red marble in the bag and goes through every combination possible and every possible marble he could pick out of every possible combination. He realises there are twelve possible outcomes and of these 4 involve him picking a red marble out of the bag. He makes no assumptions that there is a red marble in the bag and arrives at the conclusion, given the information at hand that there is a red marble in the bag. As he is not allowed to look in the bag he was correct in his probability he gave. From the marbles that were in the bag he wasn't able to pick out a red marble but because he wasn't allowed to look in the bag he had to take into account the outcomes of step one where their would have been a red marble in the bag. Bill wasn't asked if there was a red marble in the bag he was asked what was the chance of picking out a red marble, as he wasn't able to look in the bag he couldn't conclude which outcomes of step one shoul be removed and had to take into account all of them.
PART B - Here is a new puzzle for you: you and I both have a dice. I will roll a dice behind a screen and then you will roll a dice. Without looking behind the screen what is the chance that your dice roll will be exactly double that of mine? If you look at all of the possibilities of what I can roll and then see what you could roll to double it you will end up with a matrix that has 36 possible outcomes where only 3 events are "your roll will be exactly double that of mine." These are: me=1 & you=2; me=2 & you=4; me=3 & you=6; this means the odds of your roll being exactly double mine are 3 in 36 or 1 in 12. Now take a moment to relax as you are not going to like the next paragraph - it may leave you kicking yourself.
The puzzle in PART B is exactly the same concept as the puzzle in PART A (which is, of course, exactly the same concept as the actual question). There are times when your dice roll stands no chance of being double that of mine, you don't know what I roll (in fact you are specifically told not to look) and I have already rolled my dice before you work out the probabilty. Because of the fact that you aren't allowed to look at my dice you can't make any assumptions about my dice roll when you work out the probablity (you have to take into account the fact that you may have no chance of rolling exactly double in the same way that we take into account that there may not be a red marble in the bag in the original question). Don't think it's the same? Then how about I redo PART B as a story where I have rolled a 6 and you are asked (without looking at my dice roll) to work out the probablity of rolling exactly double what I roll. Of course, don't let that foot in your mouth get in the way of your pride - keep on arguing, say that the probablity of 1 in 12 is wrong.
The absolutely only thing you could possibly suggest is that the questioner in his written question should have posed the question as, "Given the situation what is the best probability of picking a red marble out of the bag that we can determine?" to convey the question he wanted to ask better. Of course given the context of the question that was written and the fact that it expressly reminds us of our situation not knowing what's in the bag (i.e. without looking in the bag) this suggestion would only benefit people who's grasp of context in communication is about as poor as, well, your understanding of the difference between ratios and fractions.
I have rather enjoyed this and thought the funniest part about it was when you claim the answer was wrong to the question asked. If anything you should actually be saying that the written question did not convey the question the questioner wanted to convey - which is a rather astounding claim considering the questioner's question was conveyed via the written question accurately and successfully to multiple people and the only person that seems to have a problem with the written question not matching the answer (and by inference the question meant to be conveyed by the questioner) is you. Have you stopped to think perhaps the problem in all of this wasn't the written question (that successfully transferred the questioner's intended question to many people) but instead was your poor communication skills? Perhaps your brain can't automatically put things into context - be thankful we have highlighted this problem of yours so you can be aware of it in the future.
you're welcome,
j-me
Here's the final final attempt:
PART A - let's have a story and say that the exercise (only involving 1 marble of each) is actually done by Bill. A machine churns out a random selection of marble and they are put into a bag, there is a green marble and a blue marble but no red marble in the bag. Bill is explained how the machine works and told how many marbles there are of each colour and asked to work out the possiblity of him picking out a red marble without looking in the bag. Bill realises that there may not be a red marble in the bag and goes through every combination possible and every possible marble he could pick out of every possible combination. He realises there are twelve possible outcomes and of these 4 involve him picking a red marble out of the bag. He makes no assumptions that there is a red marble in the bag and arrives at the conclusion, given the information at hand that there is a red marble in the bag. As he is not allowed to look in the bag he was correct in his probability he gave. From the marbles that were in the bag he wasn't able to pick out a red marble but because he wasn't allowed to look in the bag he had to take into account the outcomes of step one where their would have been a red marble in the bag. Bill wasn't asked if there was a red marble in the bag he was asked what was the chance of picking out a red marble, as he wasn't able to look in the bag he couldn't conclude which outcomes of step one shoul be removed and had to take into account all of them.
PART B - Here is a new puzzle for you: you and I both have a dice. I will roll a dice behind a screen and then you will roll a dice. Without looking behind the screen what is the chance that your dice roll will be exactly double that of mine? If you look at all of the possibilities of what I can roll and then see what you could roll to double it you will end up with a matrix that has 36 possible outcomes where only 3 events are "your roll will be exactly double that of mine." These are: me=1 & you=2; me=2 & you=4; me=3 & you=6; this means the odds of your roll being exactly double mine are 3 in 36 or 1 in 12. Now take a moment to relax as you are not going to like the next paragraph - it may leave you kicking yourself.
The puzzle in PART B is exactly the same concept as the puzzle in PART A (which is, of course, exactly the same concept as the actual question). There are times when your dice roll stands no chance of being double that of mine, you don't know what I roll (in fact you are specifically told not to look) and I have already rolled my dice before you work out the probabilty. Because of the fact that you aren't allowed to look at my dice you can't make any assumptions about my dice roll when you work out the probablity (you have to take into account the fact that you may have no chance of rolling exactly double in the same way that we take into account that there may not be a red marble in the bag in the original question). Don't think it's the same? Then how about I redo PART B as a story where I have rolled a 6 and you are asked (without looking at my dice roll) to work out the probablity of rolling exactly double what I roll. Of course, don't let that foot in your mouth get in the way of your pride - keep on arguing, say that the probablity of 1 in 12 is wrong.
The absolutely only thing you could possibly suggest is that the questioner in his written question should have posed the question as, "Given the situation what is the best probability of picking a red marble out of the bag that we can determine?" to convey the question he wanted to ask better. Of course given the context of the question that was written and the fact that it expressly reminds us of our situation not knowing what's in the bag (i.e. without looking in the bag) this suggestion would only benefit people who's grasp of context in communication is about as poor as, well, your understanding of the difference between ratios and fractions.
I have rather enjoyed this and thought the funniest part about it was when you claim the answer was wrong to the question asked. If anything you should actually be saying that the written question did not convey the question the questioner wanted to convey - which is a rather astounding claim considering the questioner's question was conveyed via the written question accurately and successfully to multiple people and the only person that seems to have a problem with the written question not matching the answer (and by inference the question meant to be conveyed by the questioner) is you. Have you stopped to think perhaps the problem in all of this wasn't the written question (that successfully transferred the questioner's intended question to many people) but instead was your poor communication skills? Perhaps your brain can't automatically put things into context - be thankful we have highlighted this problem of yours so you can be aware of it in the future.
you're welcome,
j-me
I was going to respond to this post, with another attempt to explain what I meant, but after the seventh insult to my level of intelligence in your previous two posts, I realised that you were not interested and had resorted to the actions of a 12 year old by peppering your "argument" with petty and childish insults.
At no time in my posts did I ever insult you or act condescendingly to you, yet you feel that to do such things is fine. So be it.
No, in all honesty, probability is not my strong point, that is why out of my 500+ teasers on this site, only a couple are probability.
Perhaps, we can continue this conversation in a few years time when you have matured enough to be able to conduct yourself with a modicum of civility.
Good day to you.
At no time in my posts did I ever insult you or act condescendingly to you, yet you feel that to do such things is fine. So be it.
No, in all honesty, probability is not my strong point, that is why out of my 500+ teasers on this site, only a couple are probability.
Perhaps, we can continue this conversation in a few years time when you have matured enough to be able to conduct yourself with a modicum of civility.
Good day to you.
I wasn't being insulting, I was just highlighting your lack of understanding in an attempt to knock you off that pedastool you placed yourself on. The next time you don't understand something (especially if it's in an area your not strong in like probability) then I suggest you ask questions instead of just asserting it is wrong.
I'm glad you finally understood the question and the answer and the context and I'm not surprised you felt inclined to use "maturity" as a way to end the conversation rather than having the guts to admit you were wrong and arrogant.
The day you stop pretending to be 38 is the day you may actually gain some maturity.
I'm glad you finally understood the question and the answer and the context and I'm not surprised you felt inclined to use "maturity" as a way to end the conversation rather than having the guts to admit you were wrong and arrogant.
The day you stop pretending to be 38 is the day you may actually gain some maturity.
Their are seven seperate insults in the previous two post. I am sorry you felt that you needed to resort to such low measures especially considering I was never rude to you. I was NOT debating your answer, infact I said your math was correct, only the question asked did not match the answer. I am sorry you can not seperate genuine concern from the childishness you are accostomed to. Your inability to relate maturely is your concern, not mine. please feel free to post some more of your childish, pointless and telling insults. I shall move on and I hope you have a nice life and eventually learn to grow up a little.
Have fun.
Have fun.
see above
Ditto
u r f***** too long....
i agree with mad-ade
de otha guy is jsdkahfjksah
i agree with mad-ade
de otha guy is jsdkahfjksah
It was fun reading the many comments from smart people who over thought this one yet felt compelled to argue their flawed logic.
I have to agree with Mad-Ade. the shell is definitely an integral part of the Egg.
The propabilty averages out to 1/3, no matter what. But I really liked the teaser! (Just not the people commenting who think they actually know this! )
Mad-Ade, you're the one who needs to start acting mature.
That was funny.
Lavendar, I am not the one who resorted to insults.
Give it up, maddie. Your argument has long since become a moot point. The teaser "stands" well as written.
Good teaser. I agree with the answer. I don't understand the arguments of those opposed. Let's say there was no bag. Just reach into the bin of mixed up marbles 1:1:1 and randomly clutch out anywhere from 1 to 10 marbles. Then with your dextrous hand you allow all but 1 to marble to fall away. Are you saying that there is not a 1:3 chance you will have a red marble in your hand?
How is the bag any different than the hand?
Here's another one: You are playing craps with a friend. You place your bet for whatever and you close your eyes as the dice roll. Your friend asks you why you are closing your eyes and you tell him that your odds are different if I wait until the dice have already settled onto the table. That sounds stupid, but that's what all these opposing arguments sound like to me.
And doesn't the law of averages or the law of large numbers show that over time the same experiment will converge towards the expected probability?
And you said that over time you will have 1:3 reds. Therefore you are agreeing that the expected probability is 1:3.
Hey if I can alter my odds at roulette by letting someone else randomly pick my bet, I'd like you to tell me what my new odds are.
Maybe you're on to something big.
How is the bag any different than the hand?
Here's another one: You are playing craps with a friend. You place your bet for whatever and you close your eyes as the dice roll. Your friend asks you why you are closing your eyes and you tell him that your odds are different if I wait until the dice have already settled onto the table. That sounds stupid, but that's what all these opposing arguments sound like to me.
And doesn't the law of averages or the law of large numbers show that over time the same experiment will converge towards the expected probability?
And you said that over time you will have 1:3 reds. Therefore you are agreeing that the expected probability is 1:3.
Hey if I can alter my odds at roulette by letting someone else randomly pick my bet, I'd like you to tell me what my new odds are.
Maybe you're on to something big.
Good one
In statistics, if you have a limited population, such as 3000 marbles, we can ignore any changes in the probability of a "success" as long as we draw less than 10% of that total limited population.
IE: since 300 is 10% of 3000 marbles, we can ignore any changes in probabilities due to a change in the number of marbles.
1 red marble, that means 2999 marbles in the bag, probability is now 999/2999 which is different from 1000/3000 (but not that much)
300 red marbles, that means 2700 marbles in the bag, probability is now 700/2700 which is almost nearly 1/4, as compared to the 1/3, so there is a noticable difference here.
IE: since 300 is 10% of 3000 marbles, we can ignore any changes in probabilities due to a change in the number of marbles.
1 red marble, that means 2999 marbles in the bag, probability is now 999/2999 which is different from 1000/3000 (but not that much)
300 red marbles, that means 2700 marbles in the bag, probability is now 700/2700 which is almost nearly 1/4, as compared to the 1/3, so there is a noticable difference here.
Its 1/3 argument ends FULL STOP
It never says you are drawing from the bag anyway. Only the probability w/out looking into it.
Spockinasmock, as has been pointed out a couple times in this post the expression "1:3" implies a ratio in statistics of 1 of something to every 3 of something else. In other words if you had 1 red marble and 3 blue marbles, 1/4 are red, but you could also express this as 1:3, one red for every 3 blue.
Just telling you this cause I actually thought your other comments were very insightfull and explain very well the falacy of Made-ade's arguments, but you should know this in case someone jumps all over you for it (like me hehe) or worse simply dismisses your comment as being from someone who doesn't know what they are talking about.
Just telling you this cause I actually thought your other comments were very insightfull and explain very well the falacy of Made-ade's arguments, but you should know this in case someone jumps all over you for it (like me hehe) or worse simply dismisses your comment as being from someone who doesn't know what they are talking about.
Easy, but fun.
Wow...a lot of comments for such a simple problem. The answer given is, of course, correct.
What would have made for a more interesting question would be to allow the machine to also put no marbles in the bag. Then there are 3001 possibilities of which 1000 produce a red marble giving a probability of 1000/3001.
What would have made for a more interesting question would be to allow the machine to also put no marbles in the bag. Then there are 3001 possibilities of which 1000 produce a red marble giving a probability of 1000/3001.
1 in 3 is fine as an answer. It does not assume that there are red marbles in the bag, it merely assumes that all marbles have an equal probability of being drawn. In general, making a random draw of a sample from a population and then making a random draw of an individual from the sample is equivalent to making a random draw from the population.
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