4 ms·
Why are we excluding red, green, red?
by bitshiftfaced 3y ago
Why are we excluding red, green, red?
- danielmarkbruce 3y agoYou have just highlighted the actual problem with the question. Uniform distribution.
- tines 3y agoNot really; he's hypothesizing a potential draw order, but what I was listing were the possible contents of the urn before any are drawn. Since the contents of the urn aren't ordered, they form a set, not a list, and shuffling elements doesn't add to the list of possibilities.
- danielmarkbruce 3y agoI don't think he/she is talking about that. I think the question is about the probabilities of each of the three options you lay out. You lay it out as though it's obvious the three are equally likely possibilities in the urn. That's only true using uniform distribution to generate the number of red(/green) in the urn. The contents of the urn would still be a set, but if the contents were initially drawn from a binomial distribution, calling out the possible combinations is required for purposes of counting, ie figuring the probability of each combination. People intuitively know that there are more ways to have two green and one red than three reds. That maps to most things in the real world too. This question sort of tricks people.
- tines 3y agoI thought that it was pretty clear from the part where it describes how the urn is filled: > n of them are red, and 100-n are green, where n is chosen uniformly at random in [0, 100]. N is chosen first, and that many red balls are put in. You don't flip a coin 100 times and then determine N from how many heads you flipped, that would be a tortuous interpretation from my pov, and would violate the requirement that N is chosen uniformly, so it seems like it's right there in the question.
- danielmarkbruce 3y agoIt is there. But it's just a detail many will breeze over and then their intuition fails them. The way you can know this is: ask people the same question with "binomial" instead of "uniform" and see if you get a different answer. My guess is people will say the same regardless.
- tines 3y agoI think the thing that clarifies it for me is that if the balls are chosen in such a way that they have a binomial distribution, then, intuitively, the question would be implying retrocausality by saying that N was also "chosen": > n is chosen uniformly at random If the balls follow a binomial distribution, then your intuition would say that N wasn't the thing that was chosen; the balls were chosen, and then N was determined afterwards by counting the balls that you picked. This is because you cannot choose N and then draw balls binomially and get that many green or red balls. You'd have to choose 100 balls, see whether the number of Red matches your chosen N, and if it didn't, draw again, which is a tortuous interpretation given the phrasing, as I said above. By saying that N was "chosen", it implies to me that N comes first, and the choice of balls comes after that, i.e. the balls are not binomially distributed.
- danielmarkbruce 3y agoOh, I'm not suggesting you are wrong. I'm just saying it's easy to overlook the detail.
- tines 3y agoSure, I guess I'm just arguing that even if you overlook that detail, then your intuition should tell you that the balls having a binomial distribution is suspect, i.e. you have to overlook a small thing and a big thing to misunderstand, and given that, I don't think the question is ambiguous. All good though.
- 3y ago
- tines 3y agoThe balls in the container are not ordered.
- deleted 3y ago[deleted]
- deleted 3y ago[deleted]
- AtNightWeCode 3y agoBecause it is a trick question. That state is not in play.