You have made it to the final round of “Let’s Make aDeal.” You know there is $1 million behind either door 1,door 2, or door 3. It is equally likely that the prize is behindany of the three. The two doors without a prize have nothingbehind them. You randomly choose door 2, but before door2 is opened Monte reveals that there is no prize behinddoor 3. You now have the opportunity to switch and choosedoor 1. Should you switch? Assume that Monte plays asfollows: Monte knows where the prize is and will open anempty door, but he cannot open door 2. If the prize is reallybehind door 2, Monte is equally likely to open door 1 ordoor 3. If the prize is really behind door 1, Monte mustopen door 3. If the prize is really behind door 3, Montemust open door 1. What is your decision?
You have made it to the final round of “Let’s Make a
Deal.” You know there is $1 million behind either door 1,
door 2, or door 3. It is equally likely that the prize is behind
any of the three. The two doors without a prize have nothing
behind them. You randomly choose door 2, but before door
2 is opened Monte reveals that there is no prize behind
door 3. You now have the opportunity to switch and choose
door 1. Should you switch? Assume that Monte plays as
follows: Monte knows where the prize is and will open an
empty door, but he cannot open door 2. If the prize is really
behind door 2, Monte is equally likely to open door 1 or
door 3. If the prize is really behind door 1, Monte must
open door 3. If the prize is really behind door 3, Monte
must open door 1. What is your decision?
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