An Aside: Do you think Marilyn was correct? If so, a question and a challenge for you. How smart are you? If you knew that Marilyn's argument was wrong, could you figure out why?
Consider a whole herd of women. They are all dressed in various assortments of red or blue, shirts, pants and hats. They all have two children. Women with other than two children were dressed in a different color and for the purpose of this convention were not needed..
The Red Articles: Each red article of clothing has the question:
At least one of the woman’s children is a girl. What are the chances that she has two girls?
The Blue Articles: Each blue article of clothing has the question:
At least one of the woman’s children is a boy. What are the chances that she has two boys?
The Small Print:
On the hats, in very small print it says: The woman was asked, “Do you have at least one boy?
On the pants, in very small print it says: The woman was asked, “Do you have at least one girl?
There is no small print on the shirts.
Given that a woman has a blue hat, or red pants, the answer to the question is 1/3.
Given that a woman has a red hat, or blue pants, the answer to the question is 1.
The answer to the question on the shirts is 1/2.
Does the answerer of the question have a right to the small print? Or, should the answerer be expected to guess the question?
Given that a randomly captured woman has a blue shirt, the answer to her question is 1/2. There is no small print.
Marilyn’s Error: She changed the question.
She asked the woman’s question as per the shirts.
She answered as per the hats, or the pants.