# Cecil's Mistake In "Card In Hat" Problem

**URL:** <https://boards.straightdope.com/t/cecils-mistake-in-card-in-hat-problem/487>\
**Category:** Cecil's Columns/Staff Reports\
**Created:** [January 28, 2000, 9:56pm UTC](https://boards.straightdope.com/t/cecils-mistake-in-card-in-hat-problem/487 "2000-01-28T21:56:00Z")\
**Posts on this page:** 2\
**Page:** 2

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**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\
**Post date:** [February 2, 2000, 1:02am UTC](https://boards.straightdope.com/t/cecils-mistake-in-card-in-hat-problem/487/21 "2000-02-02T01:02:00Z")

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> [@](#):
>
> Originally posted by **\<font color=#FF30c0\>CKDextHavn\</font\>** :  
> **If you give the treatment ONLY to those for whom both tests indicate that they have the disease (if even one of the tests indicate you do not have the disease, then you do not take the test), then a total of 9,850 die compared to the initial 30,000.**

Why stop there? Just give the test again, and again. Then, only maybe five will die–from the boredom of having to take the test so many times.

\<font color=#DCDCDC\>rocks\</font\>

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**Author:** ![Sam\_Stone](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Sam\_Stone](https://boards.straightdope.com/u/Sam_Stone)\
**Post date:** [February 2, 2000, 9:09am UTC](https://boards.straightdope.com/t/cecils-mistake-in-card-in-hat-problem/487/22 "2000-02-02T09:09:00Z")

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Actually, this problem may be an application of Bayes’ theorem. You are comparing two unlikely events here; there’s a one in 100 chance that you have the disease, and a 5/100 chance that the test is a false positive. So you should not take the treatment.

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