Bayes theorem, and making probability intuitive

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<div id="description" class="style-scope ytd-video-secondary-info-renderer">Perhaps the most important formula in probability. Brought to you by you: <a class="yt-simple-endpoint style-scope yt-formatted-string" spellcheck="false" href="https://www.youtube.com/redirect?redir_token=wVMkwovUiazlyL7IC1eC6_LG_2B8MTU3NzE3NTUwOEAxNTc3MDg5MTA4&q=http%3A%2F%2F3b1b.co%2Fbayes-thanks&event=video_description&v=HZGCoVF3YvM" target="blank" rel="nofollow">http://3b1b.co/bayes-thanks</a> The quick proof: <a class="yt-simple-endpoint style-scope yt-formatted-string" spellcheck="false" href="https://www.youtube.com/watch?v=U_85TaXbeIo">https://youtu.be/U_85TaXbeIo</a> Interactive made by Reddit user Thoggalluth: <a class="yt-simple-endpoint style-scope yt-formatted-string" spellcheck="false" href="https://www.youtube.com/redirect?redir_token=wVMkwovUiazlyL7IC1eC6_LG_2B8MTU3NzE3NTUwOEAxNTc3MDg5MTA4&q=https%3A%2F%2Fnskobelevs.github.io%2Fp5js%2FBayesTheorem%2F&event=video_description&v=HZGCoVF3YvM" target="blank" rel="nofollow">https://nskobelevs.github.io/p5js/Bay...</a> The study with Steve: <a class="yt-simple-endpoint style-scope yt-formatted-string" spellcheck="false" href="https://www.youtube.com/redirect?redir_token=wVMkwovUiazlyL7IC1eC6_LG_2B8MTU3NzE3NTUwOEAxNTc3MDg5MTA4&q=https%3A%2F%2Fscience.sciencemag.org%2Fcontent%2F185%2F4157%2F1124&event=video_description&v=HZGCoVF3YvM" target="blank" rel="nofollow">https://science.sciencemag.org/conten...</a> <a class="yt-simple-endpoint style-scope yt-formatted-string" spellcheck="false" href="https://www.youtube.com/redirect?redir_token=wVMkwovUiazlyL7IC1eC6_LG_2B8MTU3NzE3NTUwOEAxNTc3MDg5MTA4&q=http%3A%2F%2Fwww.its.caltech.edu%2F%7Ecamerer%2FEc101%2FJudgementUncertainty.pdf&event=video_description&v=HZGCoVF3YvM" target="blank" rel="nofollow">http://www.its.caltech.edu/_{camerer/E...</a}> You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project. ------------------ These animations are largely made using manim, a scrappy open-source python library: <a class="yt-simple-endpoint style-scope yt-formatted-string" spellcheck="false" href="https://www.youtube.com/redirect?redir_token=wVMkwovUiazlyL7IC1eC6_LG_2B8MTU3NzE3NTUwOEAxNTc3MDg5MTA4&q=https%3A%2F%2Fgithub.com%2F3b1b%2Fmanim&event=video_description&v=HZGCoVF3YvM" target="blank" rel="nofollow">https://github.com/3b1b/manim</a> If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. 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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">goalisforyoutocomeawayfromthisvideounderstandingoneofthemostimportant00</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:03formulas</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">in probability, Bayes’ theorem.00</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">formulaiscentraltoscientificdiscovery, it’s a coretool in machinelearningand00</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">, and it’s even been used for treasure hunting, when in the 80’s a small team led00</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">Tommy Thompson used Bayesian search tactics to help uncover a ship that had sunk a century00</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">half earlier carrying what, in today’s terms, amounts to $700,000,000 worth of gold.00</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">there’smorethanonelevelofunderstanding.00</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:37There’s</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">knowingwhateachpartmeans, so youcanplug in numbers.00</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:42There’s</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">understandingwhyit’strue; laterI’llshowyouto a diagramthat’shelpful00</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">rediscoveringtheformulaontheflyasneeded.00</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">there’sbeingabletorecognizewhenyouneedtouseit.00</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thegoalofgaining a deeperunderstanding, youand I will tacklethese in reverse order.01</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">beforedissectingtheformula, orexplainingthevisualthatmakesitobvious, I’dlike01</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">tellyouabout a man named Steve. Listen carefully.01</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:12Steve</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">isveryshyandwithdrawn, invariablyhelpfulbutwithverylittleinterest in people01</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">in the world of reality. A meek and tidy soul, he has a need for order and structure,</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">a passion for detail.01</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:25Which</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">ofthefollowingdoyoufindmorelikely: “Steve is a librarian”, or “Steve is01</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">farmer”?</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">ofyoumayrecognizethisas an examplefrom a studyconductedbythepsychologists01</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:35Daniel</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">KahnemanandEmosTversky, whoseNobel-prize-winningwork was popularized in bookslike “Thinking01</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">andSlow”, “TheUndoingProject”, andseveralothers.Theyresearchedhuman01</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:48judgments</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">, with a frequent focus on when these judgments irrationally contradict what the01</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">ofprobabilitysuggesttheyshouldbe.01</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">examplewith Steve, themaybe-librarian-maybe-farmer, illustratesonespecifictypeofirrationality.02</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">maybe I shouldsay “alleged” irrationality; somepeopledebatetheconclusion, butmore02</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">all that in a moment.02</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:10According</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">toKahnemanandTversky, afterpeoplearegiventhisdescriptionof Steve as “meek02</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">tidysoul”, mostsayheismorelikelytobe a librarianthan a farmer. After all,</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">02:19these</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">traitslineupbetterwiththestereotypicalviewof a librarianthanthatof a farmer.02</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">accordingtoKahnemanandTversky, thisis irrational.</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">pointisnotwhetherpeople hold correctorbiasedviewsaboutthepersonalitiesof02</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:31librarians</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">orfarmers, it’sthatalmostnoonethinkstoincorporateinformationabout02</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:36ratio</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">offarmerstolibrariansintotheirjudgments. In theirpaper, KahnemanandTversky02</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">that in the US that ratio isabout 20 to 1. Thenumbers I canfindfortodayput02</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">muchhigherthanthat, butlet’s just runwiththe 20 to 1 ratio sinceit’sa02</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">easiertoillustrate, andprovesthepoint just aswell.02</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">beclear, anyonewhoisaskedthisquestiondoesn’thaveperfectinformationonthe02</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:59actual</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">statisticsoffarmers, librarians, andtheirpersonalitytraits.Butthequestion03</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">whetherpeopleeventhinktoconsiderthis ratio, enoughtomake a roughestimate.Rationality03</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">notaboutknowingfacts, it’saboutrecognizingwhichfactsare relevant.</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">youdothinktomakethisestimate, there’s a simple waytoreasonaboutthequestion03</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">– which, spoiler alert, involves all the essential reasoning behind Bayes’ theorem.03</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">mightstartbypicturing a representative sample offarmersandlibrarians, say, 200</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">03:29farmers</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">and 10 librarians.Thenwhenyouhearthemeekandtidysouldescription, let’s03</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">your gut instinctisthat 40% oflibrarianswould fit thatdescriptionandthat 10% of03</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:40farmers</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">would.Thatwouldmeanthatfromyour sample, you’dexpectthatabout 4 librarians03</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">it, andthat 20 farmersdo.Theprobabilitythat a randompersonwhofitsthisdescription03</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">a librarian is 4/24, or 16.7%.04</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">evenifyouthink a librarianis 4 timesaslikelyas a farmerto fit thisdescription,</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">notenoughtoovercomethefactthattherearewaymorefarmers.Theupshot, and04</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">isthekeymantraunderlyingBayes’theorem, isthatnewevidenceshouldnotcompletely04</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:15determine</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">yourbeliefs in a vacuum; itshould update priorbeliefs.04</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thislineofreasoningmakes sense toyou, thewayseeingevidencerestrictsthespace04</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">possibilities, thencongratulations! YouunderstandtheheartofBayes’theorem.04</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:33Maybe</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thenumbersyou’destimatewouldbedifferent, butwhatmattersishowyoufit04</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">numberstogetherto update a belief basedonevidence.Here, seeifyoucantake a minute04</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">generalizewhatwe just didandwriteit down as a formula.04</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">generalsituationwhereBayes’theoremis relevant iswhenyouhavesomehypothesis,</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">that Steve is a librarian, andyouseesomeevidence, saythis verbal description05</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">Steve as a “meek and tidy soul”, and you want to know the probability that the05</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:06hypothesis</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">holdsgiventhattheevidenceistrue. In thestandardnotation, thisvertical05</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">means “giventhat”. As in, we’rerestrictingourviewonlytothepossibilities05</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:17where</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">theevidenceholds.05</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">first relevant numberistheprobabilitythatthehypothesisholdsbeforeconsidering05</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">newevidence. In ourexample, that was the 1/21, whichcamefromconsideringthe05</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:31ratio</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">offarmerstolibrarians in thegeneralpopulation.Thisisknownastheprior.05</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:38After</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">that, weneededtoconsidertheproportionoflibrariansthat fit thisdescription; the05</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:42probability</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">wewouldseetheevidencegiventhatthehypothesisistrue.Again, whenyou05</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thisvertical bar, itmeanswe’retalkingabout a proportionof a limitedpartofthe05</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:53total</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">spaceofpossibilities, in thiscass, limitedtotheleftslidewherethehypothesis05</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:58holds.</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">In the context of Bayes’ theorem, this value also has a special name, it’s06</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">“likelihood”.06</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:04Similarly</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">, we need to know how much of the other side of our space includes the evidence;</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">probabilityofseeingtheevidencegiventhatourhypothesisisn’ttrue.Thislittle06</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:15elbow</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">symboliscommonlyusedtomean “not” in probability.06</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">rememberwhatour final answer was. Theprobabilitythatourlibrarianhypothesis06</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">truegiventheevidenceisthe total numberoflibrariansfittingtheevidence, 4, divided06</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">the total numberofpeoplefittingtheevidence, 24.</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">06:35Where</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">doesthat 4 comefrom? Wellit’sthe total numberofpeople, timesthepriorprobability06</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">being a librarian, givingusthe 10 total librarians, timestheprobabilitythatone06</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thosefitstheevidence.Thatsamenumbershowsupagain in thedenominator, butwe06</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">toadd in the total numberofpeopletimestheproportionwhoarenotlibrarians,</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">06:57times</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">theproportionofthosewho fit theevidence, which in ourexamplegave 20.</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">total number of people in our example, 210, gets canceled out – which of course07</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">should, that was just an arbitrarychoicewemadeforillustration – leavingusfinally07</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">themoreabstractrepresentationpurely in termsofprobabilities.This, myfriends,</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">Bayes’theorem.07</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">oftenseethisbigdenominatorwrittenmoresimplyas P(E), the total probability07</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">seeingtheevidence. In practice, tocalculateit, youalmostalwayshavetobreakitdown07</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thecasewherethehypothesisistrue, andtheonewhereitisn’t.07</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:38Piling</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">onone final bitofjargon, this final answeriscalledthe “posterior”; it’s07</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">belief about the hypothesis after seeing the evidence.07</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:50Writing</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">it all out abstractlymightseemmorecomplicatedthan just thinkingthroughthe07</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:53example</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">directlywith a representative sample; andyeah, itis! Keep in mind, though, the08</div>

</div>

<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:00value</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">of a formulalikethisisthatitletsyouquantifyandsystematizetheideaofchanging08</div>

</div>

<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:06beliefs.</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">Scientistsusethisformulawhenanalyzingtheextenttowhichnewdatavalidates08</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">invalidatestheirmodels; programmersuseit in buildingartificialintelligence, where08</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">sometimeswanttoexplicitlyandnumericallymodel a machine’s belief. Andhonestlyjust08</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">howyouviewyourself, yourownopinionsandwhatittakesforyourmindtochange,</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">08:26Bayes’</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">theoremcanreframehowyouthinkaboutthoughtitself.Putting a formulato08</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">is also all themoreimportantastheexamplesgetmoreintricate.08</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:37However</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">youendupwritingit, I’dactuallyencourageyounottomemorizetheformula,</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">todraw out thisdiagramasneeded.08</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">issortofthedistilledversionofthinkingwith a representative sample wherewethink08</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">areasinsteadofcounts, whichismore flexible andeasiertosketchonthefly.08</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:54Rather</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thanbringingtomindsomespecificnumberofexamples, thinkofthespaceof08</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">possibilitiesas a 1x1square.Anyeventoccupiessomesubsetofthisspace, andthe09</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:06probability</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">ofthateventcanbethoughtaboutastheareaofthatsubset.Forexample, I09</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">tothinkofthehypothesisasfillingtheleftpartofthissquare, with a width09</div>

</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">recognizeI’mbeing a bit repetitive, butwhenyouseeevidence, thespaceofpossibilities09</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">restricted.Crucially, thatrestrictionmaynothappenevenlybetweentheleftand09</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">right. So thenewprobabilityforthehypothesisistheproportionitoccupiesin09</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">restrictedsubspace.09</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">youhappentothink a farmeris just aslikelyto fit theevidenceas a librarian,</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">theproportiondoesn’tchange, whichshouldmake sense. Irrelevant evidencedoesn’t09</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:47change</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">your belief. Butwhentheselikelihoodsareverydifferent, your belief changesa09</div>

</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">isactually a good time tostep back andconsider a fewbroadertakeawaysabout10</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">tomakeprobabilitymore intuitive, beyondBayes’theorem. First off, there’sthe10</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:24trick</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">ofthinkingabout a representative sample with a specificnumberofexamples, likeour10</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">210 librarians and farmers. There’s actually another Kahneman and Tversky result to this10</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:35effect</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">, which is interesting enough to interject here.10</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">did an experimentsimilartotheonewith Steve, butwherepeopleweregiventhe10</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:42following</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">descriptionof a fictitiouswomannamed Linda:</div>

</div>

<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">10:46Linda</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">is 31 yearsold, single, outspoken, andverybright.Shemajored in philosophy.10</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">a student, she was deeply concerned with issues of discrimination and social justice,</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">also participated in anti-nuclear demonstrations.11</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">werethenaskedwhatismorelikely: That Linda is a bankteller, orthatLinda11</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">a bank teller and is active in the feminist movement. 85% of participants said the latter11</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">morelikely, eventhoughthesetofbanktellersactive in thefemistmovementisa11</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:21subset</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">ofthesetofbanktellers!</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">, what’s fascinating is that there’s a simple way to rephrase the question that11</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:31dropped</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thiserrorfrom 85% to 0. Instead, ifparticipantsaretoldthereare 100 people11</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">fit this description, and asked people to estimate how many of those 100 are bank11</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:43tellers</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">, and how many are bank tellers who are active in the feminist movement, no one11</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:47makes</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">theerror.Everyonecorrectlyassigns a highernumbertothefirstoptionthanto11</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">second.11</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:55Somehow</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">a phrase like “40 out of 100” kicks our intuition into gear more effectively12</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">“40%”, much less “0.4”, or abstractly referencing the idea of something being more12</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">lesslikely.12</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">said, representativesamplesdon’teasilycapturethecontinuousnatureofprobability,</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">turningtoareais a nice alternative, not just becauseofthecontinuity, butalso12</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:18because</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">it’swayeasiertosketch out whileyou’repuzzlingoversomeproblem.12</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">see, peopleoftenthinkofprobabilityasbeingthestudyofuncertainty.Whilethat12</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">, of course, how it’s applied in science, the actual math of probability is really just12</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">mathofproportions, whereturningtogeometryisexceedinglyhelpful.12</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">mean, ifyoulookatBayes’theoremas a statementaboutproportions – proportions12</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">people, ofareas, whatever – onceyoudigestwhatit’ssaying, it’sactually12</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">ofobvious.Bothsidestellyoutolookat all thecaseswheretheevidenceistrue,</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">considertheproportionwherethehypothesisis also true.That’sit.That’s all it’s13</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:05saying.13</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">noteworthyisthat such a straightforwardfactaboutproportionscanbecomehugelysignificant13</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">science, AI, andanysituationwhereyouwanttoquantify belief. You’llget a better13</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:19glimpse</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">ofthisaswegetintomoreexamples.13</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">beforeanymoreexamples, wehavesomeunfinishedbusinesswith Steve. Somepsychologists13</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:28debate</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">KahnemanandTversky’sconclusion, thatthe rational thingtodoistobring13</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">mindthe ratio offarmerstolibrarians.Theycomplainthatthecontextisambiguous.13</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">is Steve, exactly? Shouldyouexpecthe’s a randomlysampledAmerican? Orwouldyou13</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">bettertoassumehe’s a friendofthesetwopsychologistsinterrogatingyou?</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">perhapssomeoneyou’repersonallylikelytoknow? Thisassumptiondeterminestheprior.13</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">, for one, run into many more librarians in a given month than farmers. And needless13</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">say, theprobabilityof a librarianor a farmerfittingthisdescriptionishighly14</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">tointerpretation.14</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">forourpurposes, understandingthemath, noticehowanyquestionsworthdebatingcan14</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">pictured in thecontextofthediagram.Questionsofcontextshiftaroundtheprior,</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">questionsofpersonalitiesand stereotypes shiftthe relevant likelihoods.14</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thatsaid, whetherornotyoubuythisparticularexperimenttheultimatepointthat14</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:25evidence</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">shouldnotdeterminebeliefs, but update them, isworthtattooing in yourmind.14</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">in no position to say whether this does or doesn’t run against natural human intuition,</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">leavethattothepsychologists.What’smoreinterestingtomeishowwecanreprogram14</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">intuitionstoauthenticallyreflecttheimplicationsofmath, andbringingtomind14</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">rightimagecanoftendo just that.14</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">is just onewaytovisualizeBayes’theorem, andI’dliketosharewithyou14</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:53another</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">waythatcanbegeneralizedtocaseswhereyouhavemorepossibilitiesthan a simple14</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">orknowfor a hypothesis, maybeeven a continuousrangeofhypotheses.Forexample,</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">youwantto update your belief aboutthemassoftheearthbasedonnewmeasurements15</div>

</div>

<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">take.We’ll also take a glimpseatthekindofconstructsprogrammersbuildontop15</div>

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<div class="cue style-scope ytd-transcript-body-renderer" tabindex="0">thisformulaasyougetmoresophisticated. All thiswiththegoaloffindingthatdeeper15</div>

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<div class="cue-group-start-offset style-scope ytd-transcript-body-renderer">:23understanding</div>

<div class="cue style-scope ytd-transcript-body-renderer active" tabindex="0">, and all of this in the next video.English</div>

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<div id="label-text" class="style-scope yt-dropdown-menu">(United States)</div>

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Bayes theorem, and making probability intuitive

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