It's definitely a poorly worded question. "More likely" is ill-defined. More likely than what? Than the last draw? Than drawing the other color just on this pick?
Yes, it's a bit of a pet peeve of mine to use the word "more" while leaving vague the point of comparison. Especially in something like a twitter poll -- twitter isn't exactly renowned as a place where people think closely about things before clicking.
How is "more likely"I'll defined? They are two options red or green. Are you more likely to draw red or are you more likely to draw green.. how is it poorly worded?
Because it could be more likely red than green, or more likely red than it was likely that the first choice was red (which is where some people got confused, they thought the question was asking about the relative chances of red on the first choice v second choice), more likely green than the first one was likely to be green(same basic problem).
You are basically asking "how could it possibly be the wrong answer?".
Yes, under that definition of "more likely", it cannot be more likely. It can be equally likely or less likely. And then weighted it would be less likely. And that would be the answer. Which is one of the choices.
No, I'm saying "Your interpretation of the sentence is obviously wrong". With that interpretation, parts of the question are nonsense. The more straightforward interpretation does not have that problem.
1 - I said it's poorly worded, I didn't interpret it that way. I could see how people would misinterpret it (as pointed out by the parent comment) and people did misinterpret it that way. Look at the other posts here. If someone posts a question in english and a bunch of english speakers misinterpret the question, it's poorly worded by definition.
2 - Exactly what parts of the question are nonsense under that interpretation?
I had the same question but the interpretation they're considering is whether the next ball you draw will be more likely to be red than the red ball you drew was likely to be red before you drew it but after the total number of red balls was already determined.
Like: you have a box with a whole bunch of red and green balls. Would removing a red ball increase or decrease the likelihood of drawing a red ball from the box in the future?
I wouldn't buy that as a reasonable misinterpretation of the question in most cases, but I don't know what standard of analysis holds for Twitter polls.
I think it's a matter of knowing that the phrase "where n is chosen uniformly at random" means something very different in a probability question than "where n is an arbitrary value".
If, hypothetically, the majority of words communicated from one homo sapiens to any other homo sapiens (majority weighted by the number of homo sapiens who will hear, read, or otherwise receive the word over the course of the word's existence) were designed to be precise and unambiguous to the extent that the mean number of homo sapiens who receive the word correctly interpret the exact meaning of the word intended by the entity that chose the word is greater than 99.99%, then I would estimate a greater than 90% probability that the cumulative unique information (in the information-theoretic sense) contained in communications correctly interpreted by the receiving homo sapiens on any given day would be less than the cumulative unique information that is currently being correctly interpreted today (January 30th 2024 in the Gregorian calendar), and furthermore the reduction in information thus communicated would have a negative effect on progress towards the majority of cumulative goals implicitly created by all living homo sapiens.
Or I could just say "I think most people interpreted the tweet correctly, and it would be annoying if it was overly precise"
