3 ms·
You 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
by seabee 16y ago
You 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.