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Quizmaster - the big prize he picks one of the other two...

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The quizmaster offers you the choice of doors 1, 2 or 3. A big prize lies behind one door (chosen at random), while the other doors hide valueless booby prizes. You arbitrarily pick door number 1; the probability that this door has the big prize is 1/3. The quizmaster now starts opening doors. To heighten suspense, the first door he opens will not be the door you picked and will not be the door with the big prize. (If you have picked the door with
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Unformatted text preview: the big prize, he picks one of the other two doors at random to open.) Let's say he opens door number 2 to reveal a booby prize. At this point, he offers to let you switch to door number 3. Should you switch? To answer this, you must figure out the conditional probability that the big prize is behind each of the doors, given the above information....
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