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→Solution using Bayes' theorem: clean up & uniformity
That is, the probability that the prize is behind door 1, given that Monty opens door 2, is 1/3, so the probability that it is behind door 3 is 2/3. Thus, the contestant should switch. The logic applies equally if Monty opens door 3.
That is, the probability that the prize is behind door 1, given that Monty opens door 2, is 1/3, so the probability that it is behind door 3 is 2/3. Thus, the contestant should switch. The logic applies equally if Monty opens door 3.
[[category:Probability and Statistics]]
[[Category:Probability and Statistics]]