# Probability Brainteaser - have I got this right?

**URL:** <https://boards.straightdope.com/t/probability-brainteaser-have-i-got-this-right/395556>\
**Category:** Factual Questions\
**Created:** [March 12, 2007, 3:48am UTC](https://boards.straightdope.com/t/probability-brainteaser-have-i-got-this-right/395556 "2007-03-12T03:48:07Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![BACI](https://avatars.discourse-cdn.com/v4/letter/b/ce73a5/32.png) [@BACI](https://boards.straightdope.com/u/BACI)\
**Post date:** [March 12, 2007, 3:48am UTC](https://boards.straightdope.com/t/probability-brainteaser-have-i-got-this-right/395556/1 "2007-03-12T03:48:07Z")

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I remember reading a brainteaser that had a counter-intuitive answer. I also remember it being discussed and confirmed in a Statistics class at one stage. I think I have the question right but I’m not sure.

Can someone please either confirm for me, or correct me on the following:

A quizmaster presents a contestant with three doors, behind one of which is a prize. The contestant chooses door A. The quizmaster, building the suspense, opens door B to reveal the prize is not there. He then askes the contestant if he wants to change his answer. The question is, should he?

The answer as I recall is that he actually has a materially greater chance of success if he does change his answer to door C. Something I think about conditional probabilities, but I can’t remember the details.

Now, I know it’s a little counter intuitive, but so is the fact that if you toss a coin and get “tails” 50 times in a row, the chances of getting tails again is still .50

Can anyone refresh me on if I’ve got the doors problem right?

Thanks so much.

M

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**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\
**Post date:** [March 12, 2007, 3:50am UTC](https://boards.straightdope.com/t/probability-brainteaser-have-i-got-this-right/395556/2 "2007-03-12T03:50:29Z")

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Do a search on the board for “Monty Hall” and you’ll find more discussion then you care to read about this question.

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**Author:** ![BACI](https://avatars.discourse-cdn.com/v4/letter/b/ce73a5/32.png) [@BACI](https://boards.straightdope.com/u/BACI)\
**Post date:** [March 12, 2007, 3:53am UTC](https://boards.straightdope.com/t/probability-brainteaser-have-i-got-this-right/395556/3 "2007-03-12T03:53:36Z")

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Lovely! Thanks for the quick response.

Question closed.

M

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**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\
**Post date:** [March 12, 2007, 4:53am UTC](https://boards.straightdope.com/t/probability-brainteaser-have-i-got-this-right/395556/4 "2007-03-12T04:53:20Z")

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**BACI**  
Here are 2 good links:

> **[lets make a deal article](https://boards.straightdope.com/sdmb/showthread.php?t=389170)**
>
> i still dont see how it could be 2/3 odds to pick the other door, i mean you eliminated 1 door, the remaining doors are still 50/50 statistically, however in actual practice the other door is more likely to be the prize. heres yet another analogy: ...

> **[Monty Hall](https://boards.straightdope.com/sdmb/showthread.php?t=383461)**
>
> http://www.straightdope.com/classics/a3\_189.html I’m fascinated by this one. The analogy is used, to describe the probability, that it’s like Monty’s offering you Door #2 AND Door #3, or just Door #1. But if he’s opening Door #3 anyway, isn’t...

The second link has even _more_ links within that.

As I’ve said before, there should be about a dozen or more SDMB pages with definitive explanations for recurring topics such as:

Where’s the missing dollar?  
The 3rd word ending in ‘gry’.  
Does .999… really equal 1? (Yes it _ **does** _ !!!)  
Page of collective nouns (murder of crows, etc)  
Page of collateral adjectives (dog = canine; rain = pluvial, etc)

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**Author:** ![samclem](https://avatars.discourse-cdn.com/v4/letter/s/a9a28c/32.png) [@samclem](https://boards.straightdope.com/u/samclem)\
**Post date:** [March 12, 2007, 11:13am UTC](https://boards.straightdope.com/t/probability-brainteaser-have-i-got-this-right/395556/5 "2007-03-12T11:13:55Z")

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Since this one’s been done to death, and the links are there, let’s close this.

**samclem** GQ moderator