Yes, the question must be very carefully worded (which is kind of my point, if I have one). In order to get the "unintuitive" outcome, there must be some eleme

Yes, the question must be very carefully worded (which is kind of my point, if I have one). In order to get the "unintuitive" outcome, there must be some element of selection (much like the Monty Hall problem has). In your formulation of the question, the GG possibility has already been eliminated because the mathematician answers "yes".