02 Oct '11 22:39>2 edits
Originally posted by wolfgang59I cannot understand your final conclusion (the one you state is clearly false).
WRONG
If that were true it would mean that every 2 child family with a daughter had a 2/3 chance of having a son and daughter.
Switch genders and we can then say every 2 child family with a son has a 2/3 chance of having a son and a daughter.
So therefore EVERY 2 child faamhaving a son and daughter - which is clearly false.
Regardless, your anlaysis here is flawed. Thomaster had basically asserted (before later retracting it) that P[family F has brother & sister | family F has a daughter named Mary] = 2/3. Regardless of whether or not he was right, your analysis assumes that P[F has brother & sister | F has a daughter named Mary] equates to P[F has brother & sister | F has at least one daughter]. But that turns out to be false, just like it is generally false that P[X | I1] equates to P[X | I2] when information I1 happens to entail I2 but I2 does not entail I1.