# The Movie 21- Statistical Question

**URL:** <https://boards.straightdope.com/t/the-movie-21-statistical-question/561093>\
**Category:** Miscellaneous and Personal Stuff I Must Share\
**Created:** [November 18, 2010, 2:54pm UTC](https://boards.straightdope.com/t/the-movie-21-statistical-question/561093 "2010-11-18T14:54:54Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Cicero](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cicero/32/3594_2.png) [@Cicero](https://boards.straightdope.com/u/Cicero)\
**Post date:** [November 18, 2010, 2:54pm UTC](https://boards.straightdope.com/t/the-movie-21-statistical-question/561093/1 "2010-11-18T14:54:54Z")

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I watched this movie the other night and am after help from some of the resident statisticians.

The scene (as I remember it was the Professor asking his students about a Game Show. There are three doors with a prize behind one door. The student was offered the choice of one door. He selected it and the game show host opens another door with no prize behind it.  
The student is offered the option to change his selection to the door he hasn’t picked. Should he do it?

The answer was ~Yes, as this door now had a 66% chance of being the correct door. (Again this is all from a cloudy memory).

Could someone explain how this was now more than 50%?

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**Author:** ![Barkis\_is\_Willin](https://avatars.discourse-cdn.com/v4/letter/b/a183cd/32.png) [@Barkis\_is\_Willin](https://boards.straightdope.com/u/Barkis_is_Willin)\
**Post date:** [November 18, 2010, 3:17pm UTC](https://boards.straightdope.com/t/the-movie-21-statistical-question/561093/2 "2010-11-18T15:17:33Z")

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Cecil Adams can explain it…but it will take him a while.

[http://www.straightdope.com/columns/read/916/on-lets-make-a-deal-you-pick-door-1-monty-opens-door-2-no-prize-do-you-stay-with-door-1-or-switch-to-3](http://www.straightdope.com/columns/read/916/on-lets-make-a-deal-you-pick-door-1-monty-opens-door-2-no-prize-do-you-stay-with-door-1-or-switch-to-3)

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**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\
**Post date:** [November 18, 2010, 3:17pm UTC](https://boards.straightdope.com/t/the-movie-21-statistical-question/561093/3 "2010-11-18T15:17:52Z")

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The classic Monty Hall problem. [Cecil explains it](http://www.straightdope.com/columns/read/916/on-lets-make-a-deal-you-pick-door-1-monty-opens-door-2-no-prize-do-you-stay-with-door-1-or-switch-to-3), after an embarassing false start. There are multiple threads in CCC if that doesn’t do it; search on “Monty Hall.” The latest thread, [“Monty Hall Redux,”](http://boards.straightdope.com/sdmb/showthread.php?t=527671) was bumped just this morning (and includes links to earlier threads).

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**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\
**Post date:** [November 18, 2010, 7:17pm UTC](https://boards.straightdope.com/t/the-movie-21-statistical-question/561093/4 "2010-11-18T19:17:48Z")

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Since there’s an active thread, I’ll close this one.

**twickster** , MPSIMS moderator