Mahesh Godavarti
1

Let's list all the possibilities (there are 8).


Top Hat          Graduation Cap          Women's Hat

    T                            T                             T

    T                            T                             H

    T                            H                             T

    T                            H                             H

    H                            T                             T

    H                            T                             H

    H                            H                             T

    H                            H                             H


Since I have revealed one of the hats covers "heads" AFTER inspecting both caps, You are left with six possibilities. (Note that I did not just pick the graduation cap by default).


That said, it is important to reveal the assumptions made to list the six possibilities:

  1. If I cannot reveal a "heads" that particular turn is cancelled and we start over.
  2. If I inspect both hats then I am obligated to reveal the "heads" regardless of whether the heads is below the Graduation cap or the women's hat.


Top Hat          Graduation Cap          Women's Hat

    T                            H                             T

    T                            H                             H

    H                            H                             T

    H                            H                             H

    T                             T                             H

    H                             T                             H


If your strategy is to not switch then the probability of winning is half. If your strategy is to switch the probability of winning is 2/3.