So, was my text book wrong?
Yes, your textbook was wrong. Marilyn expounded on this in one of her columns, and she was wrong too.

The logical mistake she made is that we don't know if it the professor was talking about the older or the younger child! Knowing this, there are two cases of boy-boy (or girl-girl) - one where he is talking about the younger and one where he is talking about the older.

Let's pretend you hear "boy" and you don't know the relative ages. You have a 1 out of 2 chance the child is the oldest or the youngest. I'll put a star by the child we are assuming to be a boy and I'll leave out the girl-girl red herring.

total  gender
      b*-b b*-g (assume prof talking about the older)
 1/2  1/4  1/4  
      b-b* g-b* (assume prof talking about the younger)
 1/2  1/4  1/4   
  1   1/2  1/2

[download]

Let's change boys/girls to heads/tails and assume that we are talking about flipping a coin. Toss a coin and we know that one of the tosses is heads, but not which one. Using the same logic your textbook presented, there are 4 possibilities - HH, HT, TH, and TT - therefore the odds are 2/3 that the other one is tails??? This is easily tested and refuted. Toss two coins without looking. Look at either one, then the other. Just knowing what one of the coins is has no impact on the probability that the other coin is heads or tails.

The bottom line is that calculating probablility is not intuitive, and the original problem is like tossing a coin. The fact that someone flips a coin and it came up heads (or girls or boys ;) has no effect of the odds of the second toss.

In reply to Re^5: Marilyn Vos Savant's Monty Hall problem (not so odd odds) by bmann
in thread Marilyn Vos Savant's Monty Hall problem by mutated

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