art educational maze puzzles
The Lady or the Tiger? Answer
Here is the answer to the lady or the tiger puzzle: the prince should pick the other door. If he sticks with the first door he picked, he has a 1/3 chance of finding the princess behind it. If he picks the other door, his chances double to 2/3.
Don't feel bad if you didn't quite get the answer. Many mathematicians didn't get it right when a version of this problem appeared in Parade magazine in 1990. The answer is a little counter-intuitive. Read on for an explanation.
Tigers, Collapsing Probabilities, and the Monty Hall problem
There are three possible scenarios for the prince from the very start: either the princess is behind the first door (1/3 chance), the second door (1/3 chance) or the 3rd door (1/3 chance). Once the prince picks a door for the first time though, the king then reveals a tiger from one of the other two doors -- so these two unpicked doors collapse into one unpicked door (minus the tiger). The two doors each had a 1/3 chance of having the princess behind them, so together that's 2/3 chance now. Think about it for a bit and it makes sense.
Another way to consider the puzzle is to imagine there were 1000 doors, with 999 tigers and one princess. The prince picks one door, and the king then reveals tigers behind 998 of the other 999 doors, leaving the prince with two choices: his original pick, or the one door left out of 999. Clearly, the prince would not want to open his original pick.
An even simpler explanation: Before the King reveals anything behind any of the three doors, there is obviously a 1/3 chance that the prince picks the correct door at the start. Since the King does not do anything to affect what is behind the door that the prince first picked, there must always be a 1/3 chance that the princess is behind this door. Therefore, after the King reduces the number of doors to just two, there has to be a 2/3 chance the princess is behind the other door -- since the probabilities must add to 1.
A variant of this problem first appeared in in Martin Gardner's Mathematical Games column in Scientific American in 1959. For a full explanation see the Monty Hall problem.
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