jimrandomh comments on A Probability Question - Less Wrong

3 Post author: JMiller 06 December 2012 05:29AM

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Comment author: jimrandomh 06 December 2012 07:02:14AM 12 points [-]

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.

Comment author: JMiller 07 December 2012 03:31:08AM 0 points [-]

Ah I did not see this post last night. Thanks.