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> The set of possibilities for two genders of two children is GG, GB, and BB. Yes, but there are two equally probable paths to arrive at (set-theoretic) GB. E
by RickHull 16y ago
> The set of possibilities for two genders of two children is GG, GB, and BB.
Yes, but there are two equally probable paths to arrive at (set-theoretic) GB. Each of these paths is equally probably to the remaining paths, BB and GG. There are 4 possible paths, and (set-theoretic) GB is the result of 2 of them.
Your application of set theory is inappropriate given 2 independent events.
- thwarted 16y agoThe question isn't what is the probability of any one of the paths, the question is about the probability of the final result. A fork in the road that joins up again gives each fork equal probability of reaching the destination.
- deleted 16y ago[deleted]
- seabee 16y agoYou can't understand the final result in isolation. Out of all men with two children, the probability that they will have two daughters is 1/4, the probability that they will have two sons is 1/4. This leaves heterogeneous offspring occurring 1/2 the time. If the man is able to make the statement "I have two kids, at least one's a boy", this puts him among the 3/4 of all men with one or two sons. The probability of a man with two sons cannot jump from 1/4 to 3/8 (half of 3/4), as you assert earlier. It's unintuitive, but it's more obvious when you negate the statement: "I have two children, but I do not have two daughters."
- carbocation 16y agoPerhaps this would offer an equally appealing explanation: if the man said, "I have two children but at least my firstborn is not a girl..." then the intuitively appealing response of 1/2 becomes roughly correct.
- thwarted 16y agoBut we're not trying to find out if this man falls into the 3/4 of all men with one or two sons, we're trying to determine if this man's two children are both boys when we know that one of them is.