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:
- If I cannot reveal a "heads" that particular turn is cancelled and we start over.
- 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.