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21 - Not 66.6%
In the opening scene, in the classroom at MIT, there are 3 blackboards with equations on them. The teacher asks the student which one is the correct formula. The student doesn't say anything until the teacher reveals one of the answers behind the board that are incorrect. The student then aswers. He states that with 3 blackboards, there was a 33.3 percent chance of success. But, with only two blackboards, his chances are 66.6 percent; the odds are in his favor. In REALITY, with only two blackboards left, his chances would only increase to 50/50.
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Avg. Rating:    3.6 of 10 - (7 votes cast)
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Contributed By:
Anonymous on 10-19-2008
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Comments:
nomad762 writes:
This is and isn't a slip-up. It should be noted that you're not accurately describing the scene. The professor puts it in the context of a gameshow, where the three chalkboard panels represent the three doors/curtains. After the student selects one, the professor then reveals that one of the other boards was an incorrect choice and offers the student the opportunity to change his selection. The student states that after his initial selection, there was a 33.3% chance that he was correct and a 66.6% chance of being wrong. By eliminating one of the non-chosen boards, it didn't change the odds of him being 33.3% correct, and therefore it was 66.6% he the other board is the correct choice. As described in the movie, this is a slip-up and the student is absolutely incorrect. After eliminating one board, the odds that either of the remaining boards is correct is 50/50. But here's the thing. In the context of the hypothetical gameshow setting the professor sets up, the student is actually correct...that it is not a 50/50 chance and that the odds ARE in his favor if he changes his selection. Detailed analysis of this scenario has concluded that when all the variables are factored in (the need for ratings, the enticement of the host, how the different doors/curtains are revealed, etc.) the odds are affected. I don't think it's actually a 66.6% (which would be an additional slipup within the movie), but the odds noticeably and significantly are in favor of changing the selection given that scenario.
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