Marilyn seems to overlook the fact that we are talking about 'a' woman. We know so, because our problem statement says so. It speaks of 'a' woman, and then speaks of 'the' woman. We can therefore say that the statement, "at least one of the woman's children is a boy" was made about 'the' woman. Acknowledgement of this fact destroys Marilyn's argument. As usual, Marilyn has neither acknowledged, nor disputed this fact.

Working model number one:

A woman has two children. The writer of the question saw one and only one, doesn't know which one, it was a boy. The writer then wrote, "A woman has two children, and at least one is a boy. What are her chances for two boys?"

The correct answer to this question is, unarguably, 1/2.

Working model number two:

A woman has two children. The writer of the question saw both children, then randomly reported the gender of one child, as per our question. The writer wrote, "A woman has two children, and at least one is a boy. What are her chances for two boys?"

The correct answer to this question is, unarguably, 1/2.

Working model for a correct answer of 1/3:

I challenge you to make this work, without adding words to our problem statement. We can get correct answer 1/3, if we select our woman from a select group. However, William Tunstall-Pedoe, wonder boy of all England says, "*We don't know* what population the woman was selected from or how she was selected. Any assumption about this is exactly that: an assumption."

Therefore, as per Pedoe, we haven't been told of selection. However, to get a correct answer of 1/3, the woman must have been selected from a special group. A woman with two children has a fifty fifty chance for two of a kind. To have a 2/3 chance for one of each, she must have been selected from a special group. The statement "at least one is" will not change those ratios.

As per Martin Gardner, 1/3 happens when "the flipper, agrees in advance, to say 'heads' every time possible, and to reflip on two tails". As we have a written question, this advance agreement must be a written agreement. It must be written into our problem statement. This would change our question. Sean MacLeod, graduate of Harvard, says that I can't claim agreement from Gardner because I haven't produced any of his work. I've quoted from his book and given page numbers.

There seems to be no working model, within the confines of our problem statement, which will give a correct answer of 1/3.

To prove me wrong, to collect on the $1000 challenge. Show me a working model that works!!!

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