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KalEl's answer[0] is more clear to me. The most natural, intuitive meaning I would attach to the question is (2), i.e., "I have two children. I have randomly se

by gpvos 2y ago

KalEl's answer[0] is more clear to me. The most natural, intuitive meaning I would attach to the question is (2), i.e., "I have two children. I have randomly selected a child by flipping a coin, and that one happens to be a boy born on a Tuesday. What is the chance I have two boys, i.e., the other child is also a boy?", so the answer would be 1/2. [0] https://math.stackexchange.com/questions/4400/boy-born-on-a-tuesday-is-it-just-a-language-trick/4409#4409 https://math.stackexchange.com/questions/4400/boy-born-on-a-...

recursive 2y ago
Intuition is in the mind of the beholder I guess. If someone told me they had two balloons, "and one of them is green", I would probably infer that the other one is not green. The next most natural interpretation for me would be that "at least one of my two balloons is green".
drdeca 2y ago
Suppose they said, “I used to be part of this club that I liked, but they had a rule that if anyone ever missed the weekly Tuesday meeting, they were kicked out, with no exceptions. I really liked that club, but being kicked out was worth it, worth it a thousand times over, to be there as my wife gave birth to my son (which happened on a Tuesday).” and at some other point imply that the two of them have two kids? (This contrived example is because the first example I thought of implied that their other child was probably not born on a Tuesday. This example avoids this because if the other child came second, the same reason for it being relevant if it was on a Tuesday doesn’t apply. Uh… hm, actually, not sure if this fixes the issue…) P([they have two sons] | [they have two kids] & [they have a son born on a Tuesday]) = P([they have two kids who are both boys] & [at least one of their two kids was a boy and born on a Tuesday] | [they have two kids])/P([at least one of their two kids was a son born on a Tuesday] | [they have two kids]) If two sons, the chance that at least one was born on a Tuesday is 13/49 . If they have one son, the chance that have a son born on a Tuesday is 7/49. So, given have two kids, chance of both boys and at least one born on a Tuesday is (1/4) * (13/49) = 13/196. Given two kids, chance that at least one son born on a Tuesday is (2/4)(7/49) + (1/4)(13/49) = 27/196 So, (13/196)/(27/196) = 13/27
tacitusarc 2y ago
I was so confused about this question and all the answers for so long, until it finally clicked. To me, this “puzzle” very obviously reads as your new acquaintance Dave volunteering some information about his kids. This means the probabilities are completely independent, and the answer is obviously 1/2. But the intention is to make it sneaky and complicated, in the style of bad, poorly worded puzzles. While it is phrased as a conversation, it is actually about drawing a sample from a random cohort, filtering based on gender and birth day, then determining the probability of the result. Which is completely different from how the puzzle is phrased.

by gpvos 2y ago

recursive 2y ago

Intuition is in the mind of the beholder I guess. If someone told me they had two balloons, "and one of them is green", I would probably infer that the other one is not green. The next most natural interpretation for me would be that "at least one of my two balloons is green".

drdeca 2y ago

Suppose they said, “I used to be part of this club that I liked, but they had a rule that if anyone ever missed the weekly Tuesday meeting, they were kicked out, with no exceptions. I really liked that club, but being kicked out was worth it, worth it a thousand times over, to be there as my wife gave birth to my son (which happened on a Tuesday).” and at some other point imply that the two of them have two kids? (This contrived example is because the first example I thought of implied that their other child was probably not born on a Tuesday. This example avoids this because if the other child came second, the same reason for it being relevant if it was on a Tuesday doesn’t apply. Uh… hm, actually, not sure if this fixes the issue…) P([they have two sons] | [they have two kids] & [they have a son born on a Tuesday]) = P([they have two kids who are both boys] & [at least one of their two kids was a boy and born on a Tuesday] | [they have two kids])/P([at least one of their two kids was a son born on a Tuesday] | [they have two kids]) If two sons, the chance that at least one was born on a Tuesday is 13/49 . If they have one son, the chance that have a son born on a Tuesday is 7/49. So, given have two kids, chance of both boys and at least one born on a Tuesday is (1/4) * (13/49) = 13/196. Given two kids, chance that at least one son born on a Tuesday is (2/4)(7/49) + (1/4)(13/49) = 27/196 So, (13/196)/(27/196) = 13/27

tacitusarc 2y ago

I was so confused about this question and all the answers for so long, until it finally clicked. To me, this “puzzle” very obviously reads as your new acquaintance Dave volunteering some information about his kids. This means the probabilities are completely independent, and the answer is obviously 1/2. But the intention is to make it sneaky and complicated, in the style of bad, poorly worded puzzles. While it is phrased as a conversation, it is actually about drawing a sample from a random cohort, filtering based on gender and birth day, then determining the probability of the result. Which is completely different from how the puzzle is phrased.