There are options in a deterministic world.Correct, but in the case when we have doubt there are at least two options to choose from. Two options are not allowed in a deterministic world.
Determinism is about how one chooses between the options ... one chooses based on the current state and one cannot avoid choosing based on the current state. In contrast, when one chooses with free-will, one can bypass or ignore the current state partially or entirely.
Then I misread the text.The information on the sign tells you that one path leads to the exit and another one to the trap but it does not tell you which path, the left or right one, leads to the trap or exit.
And I still don't understand the relevance.
What point are you trying to make?