Since 3 is impossible (Sarah knows there is at least one boy) that leaves three options. Two of those options imply a girl, the other implies a boy. Therefore, she can conclude that her probability estimate must be that it is 66.6% likely that there is a girl at home, and 33.3% likely that there is a boy.
You’ve taken a piece of information—you observe the man with a son—and half-applied it, by crossing off two daughters as a possibility, but you forgot to update the relative probability of having two boys, since you were more likely to see him with a son if he had two sons than if he had a son and a daughter.
You’ve taken a piece of information—you observe the man with a son—and half-applied it, by crossing off two daughters as a possibility, but you forgot to update the relative probability of having two boys, since you were more likely to see him with a son if he had two sons than if he had a son and a daughter.
Ah I did not see this post last night. Thanks.