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No, bobby, you miss my point entirely. The possibilities BB BG GB GG are only equally likely if you know nothing. Once you know something, they no longer apply. Your reasoning is the old reasoning, which I also accepted before I thought about it more deeply.
You're right in that given a set of options, once you know something that limits that set, those possibilities no longer apply. But as all you know is that 1) there are two siblings, and 2) one of these at least is a boy, then all you've done is reduce it to 3 possibilities; BB, BG, or GB. At this point, only one possibility leaves you with two boys, and two with a boy and a girl; 1/3 chance of there being two boys. Your assumption is that once you know a boy is there that you've removed one of the ELEMENTS of the puzzle, and that's not quite true.
The problem with your reasoning, and is is a very understandable one, is you've taken an element out of the equation without knowing which element it is you've removed, and that's important to know. If it was the first kid, you know it's either BG or BB. If it was the second, it's either GB or BB. If it is BB, the chances of a given boy being taken is only half, so you're left with a certainty of kid A being taken if it's BG (1/3 chance), a certainty of kid B being taken if it's GB (1/3 chance), or a 50/50 split of either kid being taken if it's BB (1/3 chance). So, 1/3 chance of it being two boys, 2/3 chance of it being a boy and a girl.
As you say, adding any 5 odd numbers would make it impossible, but he mentioned any 5 digits rather than numbers. We can therefore use that to get 4 odd numbers using 5 digits from the sequence that add up to 50. One I found was 1 + 5 + 9 + 35.
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