On Wed, 12 Mar 2008 00:33:19 -0700, The World Wide Wade <email@example.com> wrote:
>In article <firstname.lastname@example.org>, > quasi <email@example.com> wrote: > >> On Tue, 11 Mar 2008 21:56:27 EDT, Steven <firstname.lastname@example.org> >> wrote: >> >> >Suppose you meet me on a street corner and I introduce you to my son who is >> >with me. I inform you that I have another child at home. What is the >> >probability that my other child is a girl. >> >> The problem is not adequately specified. >> >> It depends on how the child accompanying the father is selected. >> >> If the child that accompanies the father is selected at random by a >> flip of a fair coin, then the probability that the other child is a >> girl is 1/3. > >The sample space for the children is (b b), (b g), (g b), (g g) where >the first slot is the youngest child, the second slot is the oldest. >These oredered pairs all have probability 1/4. Now we select a child >at random for a walk. We get a new sample space: (b b b), (b g g), (b >g b), (g b g), (g b b), (g g g), with the probabilities being 1/4 for >the first and last triples, and 1/8 for the others. The probability >the other child is a girl given the randomly selected child out with >daddy is a boy is thus > >p((b g b) (g b b))/p((b b b) (b g b) (g b b)) > > = (1/8 + 1/8)/(1/4 + 1/8 + 1/8) = 1/2.
Yes, you're right -- my mistake.
However, as far as I can see, for the rest of the cases I discussed, my conditional probabilities are correct.
>> If the father always chooses the younger child to go with him, then >> there is no information, so the probability that the other child is a >> girl is 1/2. >> >> Similarly, if the father always chooses the older child to go with >> him, then again there is no information, so the probability that the >> other child is a girl is 1/2. >> >> If a boy has _priority_ over a girl to go with the father, then the >> probability that the other child is a girl is 2/3. >> >> If a girl has _priority_ over a boy to go with the father, then the >> probability that the other child is a girl is 0. >> >> Thus, the probability critically depends on the selection mechanism. >> >> In the absence of any information, the problem is not well posed. >> >> Of course, in a given situation. you can always make a subjective >> judgement as to the type of selection, in which case, you can then >> derive an answer based on that extra assumption. >> >> For example, thinking about it culturally, if I _had_ to guess, I >> would guess that the father would choose to take the _younger_ child, >> in which case, the probability is 1/2.
In any case, my main point still holds -- the required probability can't be determined unless you know the method for the selecting the child who goes with the father.