probability
https://plus.maths.org/content/taxonomy/term/348
enMaking Two Tribes fairer
https://plus.maths.org/content/making-two-tribes-fairer
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John Haigh </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/17_mar_2015_-_1618/questions-icon.jpg?1426609136" /> </div>
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<p>In the TV game show <em>Two Tribes</em> teams can have unequal sizes. Is that fair?</p>
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<p><em><a href="http://en.wikipedia.org/wiki/Two_Tribes_(game_show)">Two Tribes</a></em> is a TV game show in which an initial seven contestants are whittled down to a single player, who then has the chance to win a cash prize. In each of the first three rounds, the contestants are split into two teams ("tribes'') on the basis of a fairly arbitrary criterion, such as going or not going on caravan holidays. The teams compete, and one member of the losing team is eliminated. A different criterion leads to new teams in the next round.</p><p><a href="https://plus.maths.org/content/making-two-tribes-fairer" target="_blank">read more</a></p>https://plus.maths.org/content/making-two-tribes-fairer#commentsFP-top-storyprobabilityWed, 18 Mar 2015 14:08:21 +0000mf3446329 at https://plus.maths.org/content23 and maths
https://plus.maths.org/content/23-and-maths
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<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>
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<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>
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<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/contentIn the beginning…
https://plus.maths.org/content/beginning
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Rachel Thomas </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/4/20_nov_2014_-_1356/icon.jpg?1416491810" /> </div>
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<p>Bob Wald tells us why probabilities are important in cosmology.</p>
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<p>
Scientific theories need to be tested in order to be accepted as a fully fledged piece of our scientific understanding of the world around us. To do this, you need an example of your physical system that the theory describes. Your theory should make predictions about how the physcial system will behave, and so by observing your example system you can test whether the predictions of your theory play out in reality. But in order for a theory to predict how a system will behave over time, you need to know what that system looked like at the beginning of your experiment.<p><a href="https://plus.maths.org/content/beginning" target="_blank">read more</a></p>https://plus.maths.org/content/beginning#commentsBig Bangphilosophy of cosmologyprobabilityThu, 20 Nov 2014 14:13:37 +0000Rachel6214 at https://plus.maths.org/contentPointless: The maths of TV gameshows
https://plus.maths.org/content/pointless-maths-tv-gameshows
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John Haigh </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/6_may_2014_-_1020/dice_icon.jpg?1399368036" /> </div>
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<p>One thing that makes TV game shows fun to watch is that there's usually an element of luck involved. But how (un)lucky is (un)lucky? We look at the probabilities of two popular examples.</p>
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<p><em>One thing that makes TV game shows fun to watch is that there's usually an element of luck involved. Even the brainiest of contestants needs to hedge their bets sometimes, and sometimes the result hinges on things that are totally out of their control. But how (un)lucky is (un)lucky? John Haigh looks at the probabilities of two popular examples.</em></p>
<h3>Pointless</h3>
<div class="rightimage" style="width: 250px;"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/articles/2014/haigh/dice.jpg" alt="Dice" width="250" height="250" /><p>How lucky is lucky?</p><p><a href="https://plus.maths.org/content/pointless-maths-tv-gameshows" target="_blank">read more</a></p>https://plus.maths.org/content/pointless-maths-tv-gameshows#commentsprobabilityTV game showutility functionWed, 07 May 2014 08:30:43 +0000Rachel6094 at https://plus.maths.org/contentWhy are we here?
https://plus.maths.org/content/why-are-we-here
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Rachel Thomas </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/4/24_feb_2014_-_1359/icon.jpg?1393250393" /> </div>
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<p>David Sloan calculates how likely it is that our Universe exists. He explains to us how, and why the answer can help shape our theories of physics.</p>
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<A href="http://www.damtp.cam.ac.uk/people/d.sloan/">David Sloan</a> has a great response for someone asking him what he does for a living: "I calculate how likely it is that the Universe exists." This impressive job description comes from Sloan’s role as a post-doctoral researcher at the University of Cambridge working on the project, <a href="https://plus.maths.org/content/establishing-philosophy-cosmology">Establishing the Philosophy of Cosmology</a>. The project aims to bring together philosophers and cosmologists to engage with the big philosophical questions in the area.<p><a href="https://plus.maths.org/content/why-are-we-here" target="_blank">read more</a></p>https://plus.maths.org/content/why-are-we-here#commentscosmologymeasure theoryphilosophy of cosmologyprobabilityMon, 24 Feb 2014 12:50:08 +0000Rachel6034 at https://plus.maths.org/contentStruggling with chance
https://plus.maths.org/content/struggling-chance
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Marianne Freiberger </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/28_nov_2013_-_1028/chance_icon.jpg?1385634489" /> </div>
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<p>A 1 in 14 million chance to win the lottery, a 5% risk of cancer, a 50:50 chance of heads on a coin — we deal with probabilities all the time, but do they actually mean anything? We explore the philosophy of probability and ask whether the probabilities that come up in physics differ from those in every day life.</p>
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<p>
It makes more sense to bet on a coin flip than to buy a lottery ticket. With a coin flip you have a 50:50 chance of winning but with the lottery that chance is only around 1 in 14 million. If you stand to win the same amount for the same stake, the choice is clear.</p>
<div class="rightimage" style="width: 300px;"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/articles/2013/chance/balls.jpg" alt="" width="300" height="257" /><p>1 in 14 million.</p><p><a href="https://plus.maths.org/content/struggling-chance" target="_blank">read more</a></p>https://plus.maths.org/content/struggling-chance#commentsgame of chancegame theoryphilosophy of cosmologyprobabilityFri, 29 Nov 2013 09:54:26 +0000mf3445952 at https://plus.maths.org/contentStill struggling with chance
https://plus.maths.org/content/still-struggling-chance
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Marianne Freiberger </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/28_nov_2013_-_1055/balls_icon.jpg?1385636146" /> </div>
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<p>Are there objective chances in the world?</p>
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<p><em>Previous article: <a href="https://plus.maths.org/content/struggling-chance">Struggling with chance: subjective probabilities</a>.</em></p><p><a href="https://plus.maths.org/content/still-struggling-chance" target="_blank">read more</a></p>https://plus.maths.org/content/still-struggling-chance#commentsEverett interpretationgame theoryphilosophy of cosmologyprobabilityquantum mechanicsquantum superpositionThu, 28 Nov 2013 09:50:40 +0000mf3445955 at https://plus.maths.org/contentBluffing and exploitation: An introduction to poker maths
https://plus.maths.org/content/bluffing-and-exploitation-introduction-poker-maths
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John Billingham </div>
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<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_2013_-_1243/poker_icon.jpg?1375443812" /> </div>
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<p>Is poker a game of psychology and cunning rather than strategy? We investigate the maths of bluffing.</p>
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<p>If you've never played poker, you probably think that it's a game for degenerate gamblers and cigar-chomping hustlers in cowboy hats. That's certainly what I used to think. It turns out that poker is actually a very complicated game indeed. </p>
<div class="rightimage" ><img src="/sites/plus.maths.org/files/articles/2013/poker/cards.jpg" alt="Hand of cards" width="350" height="247" />
<p style="width: 350px;">Poker originated in Europe in the middle ages. </p><p><a href="https://plus.maths.org/content/bluffing-and-exploitation-introduction-poker-maths" target="_blank">read more</a></p>https://plus.maths.org/content/bluffing-and-exploitation-introduction-poker-maths#commentsgame of chancegame theorypokerprobabilityThu, 08 Aug 2013 09:10:13 +0000mf3445927 at https://plus.maths.org/contentUnderstanding uncertainty: ESP and Bayes
https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes
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Kevin McConway </div>
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<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>
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<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>
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<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/contentUnderstanding uncertainty: ESP and the significance of significance
https://plus.maths.org/content/esp-and-significance-significance
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Kevin McConway </div>
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<p>In March 2011 a highly respected psychology journal published a paper claiming to provide evidence
for extra-sensory perception (ESP). The claim was based largely on the
results of a very common statistical procedure called significance testing. The experiments
provide an excellent way into looking at how significance testing
works and at what's problematic about it.</p> </div>
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<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> <br />
<div class="rightimage" style="width: 313px"><img src="/sites/plus.maths.org/files/articles/2012/esp/psychic.jpg" alt="Psychic" width="313" height="238" />
<p>Is there such a thing as extra-sensory perception? Image: <a href="http://en.wikipedia.org/wiki/File:PsychicBoston.jpg">Boston</a>.</p><p><a href="https://plus.maths.org/content/esp-and-significance-significance" target="_blank">read more</a></p>https://plus.maths.org/content/esp-and-significance-significance#commentsp-valueprobabilitypsychologysignificance teststatisticsunderstanding uncertaintyMon, 15 Oct 2012 14:46:34 +0000mf3445781 at https://plus.maths.org/contentUnderstanding uncertainty: Visualising probabilities
https://plus.maths.org/content/understanding-uncertainty-visualising-probabilities
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Mike Pearson and Ian Short </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/19_oct_2011_-_1700/icon_risk.jpg?1319040008" /> </div>
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<p>Probabilities and statistics: they are everywhere, but they are hard to understand and can be counter-intuitive. So what's the best way of communicating them to an audience that doesn't have the time, desire, or background to get stuck into the numbers? This article explores modern visualisation techniques and finds that the right picture really can be worth a thousand words.</p>
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<p><em>Probabilities and statistics: they are everywhere, but they are hard to understand and can be counter-intuitive. So what's the best way of communicating them to an audience that doesn't have the time, desire, or background to get stuck into the numbers? Ian Short explores modern visualisation techniques and finds that the right picture really can be worth a thousand words. </em></p><p><a href="https://plus.maths.org/content/understanding-uncertainty-visualising-probabilities" target="_blank">read more</a></p>https://plus.maths.org/content/understanding-uncertainty-visualising-probabilities#commentsCMSprobabilityriskstatisticsuncertaintyunderstanding uncertaintyvisualisationMon, 31 Oct 2011 09:09:35 +0000mf3445572 at https://plus.maths.org/contentAnyone for tennis (and tennis and tennis...)?
https://plus.maths.org/content/anyone-tennis
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Mark A. Thomas </div>
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<p>As the Wimbledon 2011 Championships hove into view, memories will be reawakened of the match of epic proportions that took place last year between the American John Isner and the Frenchman Nicolas Mahut. So just how freaky was their titanic fifth set and what odds might a bookmaker offer for a repeat?</p>
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<div class="rightimage" style="width: 430px"><img src="/sites/plus.maths.org/files/articles/2011/tennis/isner_mahut.jpg" alt="John Isner" width="430" height="181" />
<p>Nicolas Mahut (left, image <a href="http://en.wikipedia.org/wiki/File:Nicolas_Mahut_at_the_2009_Wimbledon_Championships_01.jpg">Bruno Girin</a>) and John Isner (right, image <a href="http://en.wikipedia.org/wiki/File:John_Isner_at_the_2009_US_Open_01.jpg">Charlie Cowens</a>).</p><p><a href="https://plus.maths.org/content/anyone-tennis" target="_blank">read more</a></p>https://plus.maths.org/content/anyone-tennis#commentsbernoulli trialgeometric distributionmathematics in sportprobabilitystatisticsFri, 03 Jun 2011 09:10:47 +0000mf3445487 at https://plus.maths.org/contentMeasuring catastrophic risk
https://plus.maths.org/content/misinterpretation-risk-metrics
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Shane Latchman </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/30%20Nov%202010%20-%2011%3A20/icon.jpg?1291116030" /> </div>
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<p>Insurance companies offer protection against rare but catastrophic events like hurricanes or earthquakes. But how do they work out the financial risks associated to these disasters? Shane Latchman investigates.</p>
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<h3>The notion of uncertainty</h3>
<p>In the early 19th century, the French mathematician <a href="http://www-history.mcs.st-and.ac.uk/Biographies/Laplace.html">Pierre-Simon de Laplace</a> wrote of a concept he had been thinking about for some time. The concept became known as <em>Laplace's demon</em> and was a thought experiment which sought to clearly explain the existence of uncertainty. It is described in his <em>Essai Philosophique sur les Probabilités</em> (1814) as:
</p><p><a href="https://plus.maths.org/content/misinterpretation-risk-metrics" target="_blank">read more</a></p>https://plus.maths.org/content/misinterpretation-risk-metrics#commentsconfidence intervalearthquakesinsurancemathematical modellingprobabilityriskrisk analysisstatisticsThu, 23 Dec 2010 14:36:31 +0000mf3445360 at https://plus.maths.org/contentCurious dice
https://plus.maths.org/content/non-transitiv-dice
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James Grime </div>
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<p>In this article we present a set of unusual dice and a two-player game in which you will always have the advantage. You can even teach your opponent how the game works, yet still win again!
We'll also look at a new game for three players in which you can potentially beat both opponents — at the same time!</p>
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<p>In this article we present a set of unusual dice and a two-player game in which you will always have the advantage. You can even teach your opponent how the game works, yet still win again!
Finally, we will describe a new game for three players in which you can potentially beat both opponents — at the same time!</p>
<p>Our two-player game involves two dice, but they're not the ordinary dice we're used to. Instead of displaying the values 1 to 6, each die has only two values, distributed as follows:</p><p><a href="https://plus.maths.org/content/non-transitiv-dice" target="_blank">read more</a></p>https://plus.maths.org/content/non-transitiv-dice#commentsdiceEfron's dicegamblinggame of chanceprobabilityWed, 13 Oct 2010 16:06:34 +0000mf3445330 at https://plus.maths.org/contentUnderstanding uncertainty: how psychic was Paul?
https://plus.maths.org/content/understanding-uncertainty-how-psychic-paul-octopus
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David Spiegelhalter </div>
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<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>
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<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/content