I appreciate deliberately misconstruing maths problems as much as the next person, but I don't see how you get that the probability of drawing the first bag out of the second bag is zero. There's no information indicating that...
Quick Probability Question
- Thread starter Pointlessness
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I appreciate deliberately misconstruing maths problems as much as the next person, but I don't see how you get that the probability of drawing the first bag out of the second bag is zero. There's no information indicating that...
History_Buff
Deity
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No bag has ever contained another bag. It is literally impossible.
azzaman333
meh
How do you know that the 2nd bag isn't a really big bag designed to carry many bags?
JohnRM
Don't make me destroy you
It depends. The question is incomplete. Are you twice as likely to draw a black marble as you were to draw a black marble in the first bag or are you twice as likely to draw a black marble in the second bag as you are a white marble?
If the former, the ratio is 60:0.
If the latter, the ratio is 40:20.
If the former, the ratio is 60:0.
If the latter, the ratio is 40:20.
Verarde
Pondering Wearing A Hat
Without looking at the responding posts, I believe the answer is 60:0. Why? In the first bag, you have a 50/50 shot at drawing a black marble.
2*0.50 = 1
You would then have a 1:1 chance in drawing a black marble, thus, every marble must be black.
2*0.50 = 1
You would then have a 1:1 chance in drawing a black marble, thus, every marble must be black.
[Maths teacher mode]
You shouldn't write probabilities as ratios. That would drop you marks in your Maths GCSE.
[/Maths teacher mode]
History_Buff
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I suspect you know this, since you're a reasonably intelligent dude, and we're on page two, but I just feel the need to say again, that if you read the question in its entirety, it's abundantly clear which of these two scenarios we're talking about.
If those are supposed to be odds then he's written them wrong. 1:1 would be equivalent to 0.5. I'm assuming he means 1/1.
Mise
isle of lucy
"Twice as likely" is vague enough that any of those could plausibly be what they meant. I would actually assume that they meant 40-20, because why would anyone say "twice as likely" when they actually mean "certain"? If they meant 60-0, they would not have said "twice as likely, so I would rule that out as a possibility straight away.
I need you and this kind of thinking in the Bechdel thread. Without that it's only half the fun.
History_Buff
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Except that it's clearly a math problem. It's not just going to tell you the answer.
You're not meta-gaming hard enough.
As Leoreth said, the complete phrase "twice as likely as [snip] compared to the first bag" can only really be interpreted one way. I don't really understand the final point you make there... the question is what must the number of marble be if this is the relationship between the bags. If you give away that the probability of black in bag 2 is 1 then you're not left with much of a question.
Mise
isle of lucy
Sorry I don't follow?
I didn't read it as a maths problem: it could easily be on a psychological test, a logic test, a management test, a reading comprehension test, or simply a trick question. It could even be a guy recalling something that happened at work/school/uni today, in which case he may be making fun of the guy who said "twice as likely".
I think it can be interpreted in a number of ways. The question says: "You are told that in the second bag, you are twice as likely to draw a black marble compared to the first bag." Now, if I'm told that, there's a number of ways of interpreting what that person is saying. Indeed, most people simply aren't well versed enough in statistics to make that kind of statement in the way that you are interpreting it (i.e. that if p=0.5 in bag 1, then p=1 is "twice as likely"). I can't think of a reason why someone would say that it is "twice as likely [snip] compared to the first bag" when actually they mean that it is "certain".
IMO the key part of the statement isn't "twice as likely", but "you are told that...". Without that phrase, then it's just a straight-forward maths question. With that phrase, you have to consider what that person is actually trying to communicate.
Mise
isle of lucy
Here's another simple maths question. 10 men are asked how long their penises are. Their answers, in inches, are as follows: 7, 7, 7, 7, 7.5, 7.5, 7.5, 8, 8.5, 8.5
What is the mean penis length of those 10 men?
What is the mean penis length of those 10 men?
The question on the OP is an unambiguous question with a single correct answer; it cannot be interpreted differently without assuming error. There is however a good case for suspecting that the question is being asked by someone who doesn't have a firm grasp of probability because it has a strange answer and isn't very difficult.
I think the underlying ignorance of probability that your getting at is an altogether more interesting subject that this probability question is, but I don't agree with your assertion that said probability question is vague or possessing of multiple solutions.
Mise
isle of lucy
You say "without assuming error" as if you're not adding any assumptions into your interpretation, but you are making a number of implicit, unstated assumptions in interpreting it as a maths question. For a start, you're assuming that it is a maths/probability question, and not any other type of question, like a trick question or a management test question. If a person actually did tell you all that information, and you actually did have 2 bags in front of you with a different number of balls in it, you most certainly wouldn't expect the 2nd bag to have 60 balls in it: the guy could be completely crazy, he could be a magician, he could be lying, .... etc.
There is only one interpretation of the question if you interpret the question as a probability question. Now, I realise that the thread title is "quick probability question", but it's not like that isn't open to interpretation either. I asked a simple maths question above, but it is in fact not simple, not maths, and not even a question... It was intended to demonstrate that the (now explicit) assumption that all the information you are given is true is not always a rational one.
Another simple maths question: if you take one log and saw it in half, how many logs do you have?
2, right?
But that's clearly not the right answer to that question. If you interpret it as a maths question, then obviously, you start with 1 log, split it in half, and now you have 2 logs. But if you interpret it as not a maths question, then there's a bloody good chance that the answer is not 2. Why would you only have 1 log to start with? This is the implicit assumption when interpreting it as a maths question: that the question presents all information necessary to answer the question definitively, and all the information is correct. So you assume that you only have 1 log to start with. But who has just 1 log? What kind of person has a saw, has the need to saw a log in two, the skill and equipment to saw it in two, but doesn't have more than 1 log somewhere else in his house/workshop/logging camp/factory? I can't think of a plausible reason why someone would only have 1 log to start with, and no more than that.
This is the problem with reducing data to merely a simple maths problem. It's why, if somebody actually did tell you about the 2 bags, in real life, you would -- should, at any rate -- have serious doubts about whether the person telling you the information is acting in good faith, giving you all the information, and that all the information you are given is correct. It's also why the US mortgage market collapsed in 2007/2008.
There is only one interpretation of the question if you interpret the question as a probability question. Now, I realise that the thread title is "quick probability question", but it's not like that isn't open to interpretation either. I asked a simple maths question above, but it is in fact not simple, not maths, and not even a question... It was intended to demonstrate that the (now explicit) assumption that all the information you are given is true is not always a rational one.
Another simple maths question: if you take one log and saw it in half, how many logs do you have?
2, right?
But that's clearly not the right answer to that question. If you interpret it as a maths question, then obviously, you start with 1 log, split it in half, and now you have 2 logs. But if you interpret it as not a maths question, then there's a bloody good chance that the answer is not 2. Why would you only have 1 log to start with? This is the implicit assumption when interpreting it as a maths question: that the question presents all information necessary to answer the question definitively, and all the information is correct. So you assume that you only have 1 log to start with. But who has just 1 log? What kind of person has a saw, has the need to saw a log in two, the skill and equipment to saw it in two, but doesn't have more than 1 log somewhere else in his house/workshop/logging camp/factory? I can't think of a plausible reason why someone would only have 1 log to start with, and no more than that.
This is the problem with reducing data to merely a simple maths problem. It's why, if somebody actually did tell you about the 2 bags, in real life, you would -- should, at any rate -- have serious doubts about whether the person telling you the information is acting in good faith, giving you all the information, and that all the information you are given is correct. It's also why the US mortgage market collapsed in 2007/2008.
