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The problem I have is that you're assuming that each of the 27 outcomes has equal probability, but the chance that we received the information in the way we did

The problem I have is that you're assuming that each of the 27 outcomes has equal probability, but the chance that we received the information in the way we did makes that a flawed assumption. The best analogous problem is the German Tank Problem: http://en.wikipedia.org/wiki/German_tank_problem http://en.wikipedia.org/wiki/German_tank_problem If we have destroyed a single German tank with a serial number 100, we can at least to begin to make an estimate on the size of the German force, by basically asking the question: "If they have 200 tanks, what was the chance one we randomly killed was this serial number? 500? 1000?" And then combining n=100->infinity to form a probability distribution. You can then say that there is an x% chance that Germany has 500 tanks, and a y% chance that Germany has 10,000 tanks. However - if instead, we asked 'does there exist a German tank with a serial number 100', and the answer is yes, this does NOT tell us anything past the fact that their tanks are >= 100 in number. We have the exact same information, but how it was determined changes the outcome drastically. Does that make sense?

jfager 15y ago
No, it doesn't make sense, because it doesn't apply here. We aren't estimating the count of anything. We know he has two kids, we know there are two genders, and we know there are seven days. All other relevant counts can be calculated directly from these, no estimation required. I already showed the probability that we would receive the message the way we did, assuming we're sampling fathers with two children, and its pretty low. If we drop the sampling assumption, it would go even lower. But that's irrelevant to the actual question, because we've already won that lottery. I've also shown the probability that we would get the statement we got given that the father had at least one son born on a Tuesday, but again, we already won that lottery. If you still insist, can you please stop talking in hand-wavy fake math and show some actual concrete numbers? To start, if each of the 27 possibilities are not equally likely, what are the actual probabilities and why?

jfager 15y ago

No, it doesn't make sense, because it doesn't apply here. We aren't estimating the count of anything. We know he has two kids, we know there are two genders, and we know there are seven days. All other relevant counts can be calculated directly from these, no estimation required. I already showed the probability that we would receive the message the way we did, assuming we're sampling fathers with two children, and its pretty low. If we drop the sampling assumption, it would go even lower. But that's irrelevant to the actual question, because we've already won that lottery. I've also shown the probability that we would get the statement we got given that the father had at least one son born on a Tuesday, but again, we already won that lottery. If you still insist, can you please stop talking in hand-wavy fake math and show some actual concrete numbers? To start, if each of the 27 possibilities are not equally likely, what are the actual probabilities and why?