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three curtains, one of which hid the grand prize. After the player made his selection,

the host would part one of the two remaining curtains to reveal a booby prize like a

goat. He would then offer the player the chance to switch to the remaining curtain if

he wished.

Question: Should he switch, or should he keep his original choice?

behind any one of the curtains is 1/3. Thus the probability of the prize behind his

chosen curtain is 1/3 and behind the other two curtains together is 2/3. When the

booby prize curtain is removed from the equation, the probability of the prize being

behind the two curtains not chosen remains 2/3, and now resides with the single

not-chosen curtain. Therefore, he should switch. He would double his chances of

winning.

Note: One can think of two boxes: one containing the chosen curtain (1/3

probability), the other containing the two not-chosen curtains with 2/3 probability of

the prize. Just because part of the contents of the latter box are revealed, does not

change the 2/3 probability.