Quote:
Originally Posted by obs20
Wouldn't this mean that from this point forward what are the odds of me having two boys, irregardless of birth order? Which would be 1/2
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Umm.. no. If Dan had said "My first child was a boy" (or, of course, "my second child was a boy") then the probability of him having two boys would be 1/2.
But since Dan does not specify which of his children is the boy he's mentioned, the odds of him having two boys is 1/3.
With no other information than that Dan has two children, we know that his children are one of four possibilities, giving eldest first: Boy-Boy, Boy-Girl, Girl-Boy, Girl-Girl. We /are/ making the assumption that each of these possibilities is equally likely - i.e. that the probability of any particular child being a boy is exactly 1 in 2 and that birth order doesn't affect this probability.
When Dan says "I have a least one boy" this is equivalent to saying "I don't have two girls". It only eliminates one of the four possibilities, leaving use with three, equally likely, remaining possibilities.
If Dan said "The eldest is a boy", that would eliminate two of the possibilities (GB GG) leaving us with only two remaining, equally likely, possibilities.
[EDIT: See my later post where I explain why we're both wrong - I wave the wrong answer, and you have the right answer for the wrong reason
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