3 ms·
The 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
by thwarted 16y ago
The 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.