conditional probability
https://plus.maths.org/content/taxonomy/term/465
enMaths in a minute: Bayes' theorem
https://plus.maths.org/content/maths-minute-bayes-theorem
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
Rachel Thomas </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="99" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/4/25_jan_2016_-_1440/icon.jpg?1453732842" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
<p>It would be foolish to ignore evidence. Luckily Bayes' theorem shows us how to take it in into account.</p>
</div>
</div>
</div>
<p>
Suppose that a particular type of cancer affects 1% of the population. There is a test for this cancer but it's not perfect: although the test gives a positive result for 90% of people who have the cancer, it also gives a positive result for 5% of the people who are cancer-free. You have just received a positive test result – what is the probability you have cancer?
</p><p><a href="https://plus.maths.org/content/maths-minute-bayes-theorem" target="_blank">read more</a></p>https://plus.maths.org/content/maths-minute-bayes-theorem#commentsbayes theoremconditional probabilityMaths in a minutemedical statisticsMon, 25 Jan 2016 14:26:40 +0000Rachel6521 at https://plus.maths.org/content23 and maths
https://plus.maths.org/content/23-and-maths
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/9_dec_2014_-_1109/crowd_icon.jpg?1418123365" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
<p>The company 23andMe made headlines by launching its DNA testing service in the UK. But how are the risks of developing a disease calculated?</p>
</div>
</div>
</div>
<p>Last week the
company <a
href="https://www.23andme.com/">23andMe</a> generated
headlines by launching its personalised DNA testing service in the
UK. If you'd like to know your risk of developing a range of diseases,
all you need to do is request a testing kit, take a saliva sample,
send it off, and await the results. </p><p><a href="https://plus.maths.org/content/23-and-maths" target="_blank">read more</a></p>https://plus.maths.org/content/23-and-maths#commentsconditional probabilitymedical statisticsmedicine and healthoddsprobabilityTue, 09 Dec 2014 10:49:47 +0000mf3446254 at https://plus.maths.org/contentUnderstanding uncertainty: ESP and Bayes
https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
Kevin McConway </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/5_oct_2012_-_1621/icon_heads.jpg?1349450461" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
<p>In the previous article we looked at a psychological study which claims to provide evidence that certain types of extra-sensory perception exist, using a statistical method called significance testing. But do the results of the study really justify this conclusion?</p>
</div>
</div>
</div>
<br />
<div align="center" style="margin:auto;width:400px; font-size:15; border: #9a7a9f 2px solid; padding:5px;">This article has been adapted from material on the <a href="http://understandinguncertainty.org/node/1286">Understanding Uncertainty website</a>.</div> <p><a href="https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes" target="_blank">read more</a></p>https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes#commentsbayes theoremconditional probabilityp-valueprobabilitypsychologysignificance teststatisticsunderstanding uncertaintyMon, 15 Oct 2012 15:48:39 +0000mf3445782 at https://plus.maths.org/contentThe logic of drug testing
https://plus.maths.org/content/logic-drug-testing
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
John Haigh </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/2_aug_2012_-_1124/icon-12.jpg?1343903097" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
<p>London 2012 vowed to be the cleanest Olympics ever, with more than 6,000 tests on athletes for performance enhancing drugs. But when an athlete does fail a drug test can we really conclude that they are cheating? John Haigh does the maths.</p>
</div>
</div>
</div>
<p><em> London 2012 vowed to be the cleanest Olympics ever, with more than 6,000 tests on athletes for performance enhancing drugs. But when an athlete does fail a drug test can we really conclude that they are cheating? John Haigh does the maths. (You can also look at the <a href="https://plus.maths.org/content/logic-drug-testing#animation">animation below</a> to see the results illustrated.)</em></p><p><a href="https://plus.maths.org/content/logic-drug-testing" target="_blank">read more</a></p>https://plus.maths.org/content/logic-drug-testing#commentsbayes theoremconditional probabilityfalse positivemathematics in sportolympicsThu, 02 Aug 2012 10:23:50 +0000mf3445757 at https://plus.maths.org/contentUnderstanding uncertainty: how psychic was Paul?
https://plus.maths.org/content/understanding-uncertainty-how-psychic-paul-octopus
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
David Spiegelhalter </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/5%20Oct%202010%20-%2012%3A47/icon.jpg?1286279224" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
<p>England's performance in the World Cup last summer was thankfully overshadowed by the attention given to Paul the octopus, who was reported as making an unbroken series of correct predictions of match winners. David Spiegelhalter looks at Paul's performance in an attempt to answer the question that (briefly) gripped the world: was Paul psychic?</p>
</div>
</div>
</div>
<p> </p> <div style="text-align:center;margin-right: auto; margin-left: auto; width: 90%; font-size: 15px; border: 2px solid #9a7a9f; padding: 5px;">This article is adapted from material on the <a href="http://understandinguncertainty.org">Understanding Uncertainty website</a>.</div><p> </p><p><a href="https://plus.maths.org/content/understanding-uncertainty-how-psychic-paul-octopus" target="_blank">read more</a></p>https://plus.maths.org/content/understanding-uncertainty-how-psychic-paul-octopus#commentsbayes theoremCMSconditional probabilitymathematics in sportprobabilityunderstanding uncertaintyFri, 08 Oct 2010 10:47:02 +0000mf3445319 at https://plus.maths.org/contentSurvival odds: are all soldiers equal?
https://plus.maths.org/content/os/latestnews/jan-apr10/army/index
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="icon" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/4/8%20Jul%202010%20-%2011%3A12/icon.jpg?1278583974" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
<p>Being killed in a peacekeeping mission apparently depends on your nationality, at least if you're a soldier in the Spanish army. On the 1st of February 2010 the Colombian soldier John Felipe Romero serving in the Spanish army was killed in a terrorist attack in Afghanistan. It was then made public that so far 43% of the Spanish troops killed in attacks by local forces in Afghanistan and Lebanon have been foreigners. This is in striking contrast to the fact that foreign nationals make up only 7% of the Spanish army as a whole.</p>
</div>
</div>
</div>
<br clear="all">
<div class="rightimage" style="width: 300px;"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/latestnews/jan-apr10/army/iStock_helmet.jpg" alt="Helmet" width="300" height="199" /> <!-- image from http://www.istockphoto.com/ --></div> <p>Being killed in a peacekeeping mission apparently depends on your nationality, at least if you're a soldier in the Spanish army. On the 1st of February 2010 the Colombian soldier John Felipe Romero serving in the Spanish army was killed in a terrorist attack in Afghanistan.<p><a href="https://plus.maths.org/content/os/latestnews/jan-apr10/army/index" target="_blank">read more</a></p>https://plus.maths.org/content/os/latestnews/jan-apr10/army/index#commentsbayes theoremconditional probabilitystatisticsSun, 25 Apr 2010 23:00:00 +0000plusadmin5214 at https://plus.maths.org/contentThomas Bayes & Mr Zootpooper
https://plus.maths.org/content/thomas-bayes-mr-zootpooper
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
Phil Wilson </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue32/features/wilson/icon.jpg?1099267200" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
The three door problem has become a staple mathematical mindbender, but even if you know the answer, do you really understand it? <b>Phil Wilson</b> lets his imagination run riot in this intergalactic application of Bayes' Theorem. </div>
</div>
</div>
<div class="pub_date">November 2004</div>
<!-- plusimport -->
<br clear="all" />
<p><i>It is the year 2057 and you are sitting in a vast auditorium beneath a night sky like nothing on Earth.<p><a href="https://plus.maths.org/content/thomas-bayes-mr-zootpooper" target="_blank">read more</a></p>https://plus.maths.org/content/thomas-bayes-mr-zootpooper#comments32bayes theoremconditional probabilitythree door problemMon, 01 Nov 2004 00:00:00 +0000plusadmin2257 at https://plus.maths.org/contentThe best medicine?
https://plus.maths.org/content/best-medicine
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
Deborah Ashby and Adrian Smith </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue22/features/medical/icon.jpg?1036108800" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
To make hard decisions, you need hard facts. <b>Medical statistics</b> can help us to decide what treatment to look for when we are ill, and to estimate our chances of recovery. </div>
</div>
</div>
<div class="pub_date">November 2002</div>
<!-- plusimport -->
<br clear="all" />
<!-- #include virtual="../../../include/gifd_here_box.html" -->
<h2>Hard questions</h2>
<p><!-- FILE: include/rightfig.html --></p>
<div class="rightimage" style="width: 300px;"><img src="/issue22/features/medical/stethoscopedhd.jpg" alt="stethoscope" width="300" height="250" />
<p>There are other diagnostic tools<br />
<font size="-1">[Image <a href="http://www.hd.org/Damon/photos/index.html">DHD Photo Gallery</a>]</font></p><p><a href="https://plus.maths.org/content/best-medicine" target="_blank">read more</a></p>https://plus.maths.org/content/best-medicine#comments22clinical trialconditional probabilitymedical statisticsmedicine and healthmeta-analysisFri, 01 Nov 2002 00:00:00 +0000plusadmin2214 at https://plus.maths.org/contentBeyond reasonable doubt
https://plus.maths.org/content/beyond-reasonable-doubt
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
Helen Joyce </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue21/features/clark/icon.jpg?1030834800" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
In 1999 solicitor Sally Clark was found guilty of murdering her two baby sons. Highly flawed statistical arguments may have been crucial in securing her conviction. As her second appeal approaches, <i>Plus</i> looks at the case and finds out how courts deal with statistics. </div>
</div>
</div>
<div class="pub_date">September 2002</div>
<!-- plusimport -->
<br clear="all" />
<!-- #include virtual="../../../include/gifd_here_box.html" -->
<!-- FILE: include/rightfig.html -->
<div class="rightimage" style="width: 331px;"><img src="/issue21/features/clark/sally1a.jpg" alt="The Clarks" width="331" height="400" />
<p>Happier days - a family snapshot of Sally and Steve Clark when they were expecting Christopher</p><p><a href="https://plus.maths.org/content/beyond-reasonable-doubt" target="_blank">read more</a></p>https://plus.maths.org/content/beyond-reasonable-doubt#comments21bayes theoremconditional probabilitySat, 31 Aug 2002 23:00:00 +0000plusadmin2208 at https://plus.maths.org/contentCars in the next lane really do go faster
https://plus.maths.org/content/cars-next-lane-really-do-go-faster
<div class="field field-type-text field-field-author">
<div class="field-items">
<div class="field-item odd">
Nick Bostrom </div>
</div>
</div>
<div class="field field-type-filefield field-field-abs-img">
<div class="field-items">
<div class="field-item odd">
<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue17/features/traffic/icon.jpg?975628800" /> </div>
</div>
</div>
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
Yes, you were right to wish you were in the other lane during this morning's commute! <b>Nick Bostrom</b> tells why we're usually caught in the slow lane. </div>
</div>
</div>
<div class="pub_date">Nov 2001</div>
<!-- plusimport -->
<br clear="all" />
<p>When driving on the motorway, have you ever wondered about (and cursed) the fact that cars in the other lane seem to be getting ahead faster than you? You might be inclined to account for this by invoking Murphy's Law ("If anything can go wrong, it will", discovered by Edward A. Murphy, Jr, in 1949).<p><a href="https://plus.maths.org/content/cars-next-lane-really-do-go-faster" target="_blank">read more</a></p>https://plus.maths.org/content/cars-next-lane-really-do-go-faster#comments17anthropic principlebayes theoremconditional probabilitydata samplingdiffusionequilibriumestimationobservation selection effectthermodynamicsFri, 01 Dec 2000 00:00:00 +0000plusadmin2194 at https://plus.maths.org/contentYe banks and Bayes
https://plus.maths.org/content/ye-banks-and-bayes
<div class="field field-type-text field-field-abs-txt">
<div class="field-items">
<div class="field-item odd">
<p>Are you going to be a good customer for your bank? This might not worry you, but it certainly worries your bank! Banks would like to be able to predict both who their most profitable clients are likely to be, and which potential clients are most likely to be unreliable or a poor risk.</p>
</div>
</div>
</div>
<div class="pub_date">
September 1999
</div><!-- plusimport --><br clear="all" />
<p><a href="https://plus.maths.org/content/ye-banks-and-bayes" target="_blank">read more</a></p>https://plus.maths.org/content/ye-banks-and-bayes#commentsbayes theoremconditional probabilityprobabilityTue, 31 Aug 1999 23:00:00 +0000plusadmin2679 at https://plus.maths.org/contentThe taxi problem revisited
https://plus.maths.org/content/taxi-problem-revisited
<div class="pub_date">January 1998</div>
<!-- plusimport --><br clear="all"></br>
<p>In this issue's article "<a href="/issue4/stander/index.html">Image analysis - a modern application of mathematics</a>", Julian Stander introduced the idea of using Bayes' Theorem to update our beliefs based on new information.</p>
<p>We can use Bayes' Theorem to solve the taxi problem in Issue No. 2 (see "<a href="/issue2/puzzle/taxi.html">The taxi problem</a>" ):</p><p><a href="https://plus.maths.org/content/taxi-problem-revisited" target="_blank">read more</a></p>https://plus.maths.org/content/taxi-problem-revisited#commentsbayes theoremconditional probabilitypuzzleThu, 01 Jan 1998 00:00:00 +0000plusadmin2921 at https://plus.maths.org/contentThe taxi problem
https://plus.maths.org/content/taxi-problem
<div class="pub_date">May 1997</div>
<!-- plusimport --><br clear="all"></br>
<p>A witness sees a crime involving a taxi in Carborough. The witness says that the taxi is blue. It is known from previous research that witnesses are correct 80% of the time when making such statements. The police also know that 85% of the taxis in Carborough are blue, the other 15% being green. What is the probability that a blue taxi was involved in the crime?</p><p><a href="https://plus.maths.org/content/taxi-problem" target="_blank">read more</a></p>https://plus.maths.org/content/taxi-problem#commentsconditional probabilityprobabilitypuzzleWed, 30 Apr 1997 23:00:00 +0000plusadmin2858 at https://plus.maths.org/content