Sometimes I hate these types of problems - though they're quite fun to argue about - because though they seem to be simple, straightforward enumeration problems, the "right" answer depends on assumptions about how the information that you've got is obtained, and what the other possible pieces of information you could have obtained are.
Here's the thing: nobody needs to see how you obtained your answer, we're all smart enough to enumerate things, so don't bother; similarly, leave out the equations, they're simple enough, and that's not where anyone falls over. If you want to argue productively about this type of problem, you need to explain why you enumerate the possibilities the way you do, not how.
And actually, I think the article goes through this problem pretty well, as mentioned there it hinges on two questions:
1) In this "random sampling", was "girl" a possible answer? Or did we restrict the sample pool to only people with boys, and only let them reveal that they had a boy?
2) Similarly, was any day other than "Tuesday" a possible answer?
Once people agree what the "obvious" answers to these questions are, disagreements tend to evaporate very quickly, and the enumerations/equations solve themselves. Unfortunately these assumptions are almost never spelled out in the problem, which is why these damn problems keep confusing people...
Here's the thing: nobody needs to see how you obtained your answer, we're all smart enough to enumerate things, so don't bother; similarly, leave out the equations, they're simple enough, and that's not where anyone falls over. If you want to argue productively about this type of problem, you need to explain why you enumerate the possibilities the way you do, not how.
And actually, I think the article goes through this problem pretty well, as mentioned there it hinges on two questions:
1) In this "random sampling", was "girl" a possible answer? Or did we restrict the sample pool to only people with boys, and only let them reveal that they had a boy?
2) Similarly, was any day other than "Tuesday" a possible answer?
Once people agree what the "obvious" answers to these questions are, disagreements tend to evaporate very quickly, and the enumerations/equations solve themselves. Unfortunately these assumptions are almost never spelled out in the problem, which is why these damn problems keep confusing people...