Consider a slight alteration in the parameters of the Monty Hall problem. In this variation after revealing to the subject the empty container he was not pointing to, we once again ask whther his probability of selecting the correct container (from the remaining two) would be greater if he switched his selection to the other (of the remaining two) containers he Is not pointing two, or whther he should stay with his initial choice.
But in this variation we make the following changes:
1. Case 1. : if his initial selection is the correct one, we serruptitiously switch the prize to the other container he is not pointing to. Thereby insuring that if he sticks with his first choice he will be wrong, but if he switches he will be right.
Case 2. : if his initial selection is not the correct one (I.e., he is pointing at an empty container), we serruptitiously switch the prize to the container he is pointing to. Thereby insuring that if he sticks with his initial choice he will be right, but if he switched he would be wrong.
Consider the probabilities of a successfull choice in the original scenario as compared to Cases 1 and 2.
I think I understand the question but somehow I don't think my answer is what you ask for.
If we are speaking objective probability, P(Success|Switching)=1 and 0. If we are speaking subjective probability, since the subject knows nothing about the changes the probability is still P(Success|Switching)=2/3 in both cases.
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