Quote:
A guest in a price show is shown three closed lockets. He is informed that only one of the lockets contain the price and is asked to make a pick. After he has chosen the host opens one of the other lockets and reveals it to be empty. He then asks the guest if he wants to change his choice.
Which of the following is true
1) It is smartest to stick with his initial choice
2) It is smartest to switch his choice
3) It doesn't matter. The chance is equal
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a couple of questions that are muddled by the question itself and haven't been sufficiently answered.
1: does the host reveal his pick to the guest, or just the audience
2: if it is shown to the guest is it revealed that the hosts choice is empty does it not remove it from the realm of possible choices bringing the number of possible locations for the locket down to 2 from 3 (the one he's chosen or the one he hasn't).
If he shows the emtpy one then there are 2 possibilities, it is in the one he chose, or it is not, and he then as 2 choices, stay or change. which still leaves a 50% chance of either being wrong.
If the host does not show the guest whether or not the one he (the host) chose then his chance is 1 in 3 of any particular choice being correct.