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The Christmas Eve Eve, statistical dilemma
The answer is C.
You should always change your mind and take the box that the quiz master left. That's because of the three scenarios possible for the quiz master, two of the three always involve the box that he leaves as being the big prize box. Therefore you increase your chances to two out of three of being correct if you change your mind. If you stick with your initial choice, you stay with the one in three chance.
It's a bit like when I go for a run. If I do an out and back, I increase the chances that I will get injured at the furthermost point from home. If I do a number of smaller loops, I instead increase my chances of feeling knackered after one loop, pulling out, commiserating with beer and ice cream (not simultaneously) and feeling wretched for the rest of the day. If however, I email SP and ask for advice, I know I increase my chances of success if I do the exact opposite to what he suggests.
Of course if I just stay home and read the RC Forum, I even further increase my chances of failure by getting stuck in threads like this... er... hmm...
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