3 ms·

Why would n be "uniformly randomly chosen" but then suddenly be known? I would mark this mis interpretation simply as wrong if I was a teacher.

tqi 3y ago
That's definitely fair, and I assuming in a classroom setting you'd be very consistent and precise about what that means. But this is a twitter poll, and I doubt people are that consistent. Ultimately I'm just pushing back on the conclusion that this is because "Bayesian thinking is really foreign to people." I think if the question had instead been "would you bet on the urn having started out with more red balls, green balls, or equal number of balls" the distribution would have been very different.
- travisjungroth 3y ago
  That question is quite a bit of handholding. A closer analogue would be “would you bet the next ball is red / green / they’re equally likely?”. Personally I’d word it as “The next ball is… more likely to be red than green / more likely to be green than red / equally likely to be red or green / I don’t know.”
  - chrismcb 3y ago
    But isn't that exactly how it is worded? Just showing it a bit?
    - travisjungroth 3y ago
      Not quite. People are arguing that “more likely to be red” can be interpreted as “more likely to be red than it was last time”. I guess you could do that with this wording, but that seems like quite a stretch.
thornewolf 3y ago
i personally would throw out the question if i was a teacher. i still feel it's ambiguous
dsizzle 3y ago
Another way of making your point: it would also make the information about the distribution of n irrelevant, so it's a bad interpretation of the question.
- rrobukef 3y ago
  So? There's plenty of problem statements with irrelevant data. Children are also getting taught to determine which is relevant in class. But also, it's not irrelevant because for two cases the probability stays equal. Calculating the exact chance is still an interesting problem and it could have been dumbed down for twitter only.
  - dsizzle 3y ago
    In those cases presumably there's not a more interesting question that's consistent with the question and that uses that information. I'd start with the assumption that the tweet isn't a dumb trick question.
- livrem 3y ago
  Because including some pieces of irrelevant information as red herrings in probability problems is totally unheard of?
rrobukef 3y ago
You have an urn of 50 red and 50 green balls. Roll a die and add a red ball for every pip. What is the probability of the next ball you take being red? I say both can be a question in Statistics I where you calculate probabilities based on combinations. So I'll say it depends on the level of education for how the question gets interpreted and saying those who never took Bayesian reasoning and consider n unknown are wrong gets elitist.
ajot 3y ago
Not known, but certainly defined. It has to not be zero at least, otherwise you couldn't take out a red ball in the first place. Or at least that's how I understand this problem. You don't know what number n is, so you need statistics or simulations to grasp the probability of the color of the next ball.

tqi 3y ago

That's definitely fair, and I assuming in a classroom setting you'd be very consistent and precise about what that means. But this is a twitter poll, and I doubt people are that consistent. Ultimately I'm just pushing back on the conclusion that this is because "Bayesian thinking is really foreign to people." I think if the question had instead been "would you bet on the urn having started out with more red balls, green balls, or equal number of balls" the distribution would have been very different.

travisjungroth 3y ago
That question is quite a bit of handholding. A closer analogue would be “would you bet the next ball is red / green / they’re equally likely?”. Personally I’d word it as “The next ball is… more likely to be red than green / more likely to be green than red / equally likely to be red or green / I don’t know.”
- chrismcb 3y ago
  But isn't that exactly how it is worded? Just showing it a bit?
  - travisjungroth 3y ago
    Not quite. People are arguing that “more likely to be red” can be interpreted as “more likely to be red than it was last time”. I guess you could do that with this wording, but that seems like quite a stretch.

thornewolf 3y ago

i personally would throw out the question if i was a teacher. i still feel it's ambiguous

dsizzle 3y ago

Another way of making your point: it would also make the information about the distribution of n irrelevant, so it's a bad interpretation of the question.

rrobukef 3y ago
So? There's plenty of problem statements with irrelevant data. Children are also getting taught to determine which is relevant in class. But also, it's not irrelevant because for two cases the probability stays equal. Calculating the exact chance is still an interesting problem and it could have been dumbed down for twitter only.
- dsizzle 3y ago
  In those cases presumably there's not a more interesting question that's consistent with the question and that uses that information. I'd start with the assumption that the tweet isn't a dumb trick question.
livrem 3y ago
Because including some pieces of irrelevant information as red herrings in probability problems is totally unheard of?

rrobukef 3y ago

You have an urn of 50 red and 50 green balls. Roll a die and add a red ball for every pip. What is the probability of the next ball you take being red? I say both can be a question in Statistics I where you calculate probabilities based on combinations. So I'll say it depends on the level of education for how the question gets interpreted and saying those who never took Bayesian reasoning and consider n unknown are wrong gets elitist.

ajot 3y ago

Not known, but certainly defined. It has to not be zero at least, otherwise you couldn't take out a red ball in the first place. Or at least that's how I understand this problem. You don't know what number n is, so you need statistics or simulations to grasp the probability of the color of the next ball.