Women Or Tigers? — The Fourth Challenge

This challenge was a favourite of the king’s.

The signs on the doors for the second prisoner to choose between read:

ROOM I: IT WON’T MAKE A DIFFERENCE WHICH DOOR YOU CHOOSE

ROOM II: THERE IS A WOMAN IN THE OTHER ROOM

Remember that if there was a woman behind door #1, the sign on the door told the truth — but if there was a tiger behind it, the sign told a lie. As for the sign on door #2, it was the opposite: If there was a woman behind it, the sign would be false, and if there was a tiger behind it, the sign would be true.

Also remember that both rooms might contain a woman, or both a tiger, or of course there might be a woman in one room and a tiger in the other.

What would you choose, if you were in this prisoner’s shoes?