Okay, this one's a bit tough to explain. There certainly are many ways to show the answer.
The probability that Chris chose the right door to start with is 1/3.
Therefore, the probability that one of the other two doors holds the prize (the Kamei puzzles) is 2/3.
However, once one of these doors is open, the probability that the remaining, un-chosen door, contains the prize must be 2/3.
So, you now have the original door, with 1/3 odds, vs. the other door, with 2/3 odds. Therefore, its much better to switch!
Don't believe us? This problem is so famous in the mathematics community there are many web-sites devoted to it:
 | WWW Tackles the Monty Hall Problem (a list of sites dedicated to the problem) |
| Monty Hall Dilemma contains a simulation of the problem |
If you don't like the solution to this problem, please don't e-mail us! Go e-mail one of those other websites!
