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PUZZLE -- WHICH CURTAIN?
In the TV show "Let's Make a Deal", the host would offer the contestant a choice of
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
Question: Should he switch, or should he keep his original choice?
SCROLL DOWN FOR SOLUTION:
SOLUTION: At the time he makes his first choice, the probability of the prize being
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
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.