 In this case, Cathy’s information partition is a refinement of the partition she has when there is no announcement, for in this case, then Cathy knows a priori that if \(\omega_1\) is the case there will be no announcement and will know immediately that she is clean, and Cathy knows a priori that if \(\omega_2\) is the case, then she will know immediately from the cook’s announcement that she is messy.