本字幕由TME AI技术生成
welcometoyourdeepdiveintotheworldofprobability
oh yeah
todayweregoingtobecheckingouttheideasinamereexellsbookcantsaguidegamamlinglolovethestock
andandmuchaboutprielsesogoodoneitissogetreadyforsomesurprisingstuffabouthowchanceshapesourlives
itsamazinghowmuchprobabilityreallydoesjustimpactourdailydecisions
itreallyisthinkaboutitrightahwereconstantlywyingodds
butthatevenrealizingitwearewhetheritschoosingaroutetoavoidtrafficorlikedecidingwhentobuyaasasitswholeprobability
itisthatsjustscratchingthesurfacethoughrightthisdeepdiveisgoingtotakeyourunderstandinghopefullytothenextleveltotallyfrombasiccalculationstolikeminebendingparadoxes
andandsortofstuffthisbookblewmymindwith
withideideaandallsorimals
yeah
myinstinctivelyuseprobabilityinterestingXLtalksabouthowapredatorstockingitspreyhastochoosethepathwiththehighestchanceofsuccessrightevenifitsnotdoingcomplexcalculationsinitsheadexactlyrightitsuggestfundamentalunderstandingofwhatslikely
yeah
thatgoesbeyondhumanreasoningrightbuthowaboutyouknowwelaysomegroundworworkitsbutwhatstsffindprobabilityfirstokayitssimplythemeasureofhowlikelyandeventistooccurexpressedasapercentagefromzeropercentimpossible
twohundredpercentcertain
sowhenisayimahundredpercent
sureilockedthedoorrightimreallymakingaprobabilitystatement
youarewow
andyouuse
youknowbasicprobability
everydayidoyoureallydo
evenlikepickingalotteryticket
yeah
involvesassessingaweversmallright
thechancesofokthatmakessense
buthowdowemovebeyondgoodfeelingsrightandactuallymeasureprobabilitysoonesimplemethodiscountingoutcomesokay
ifalloutcomesarelikekelyyoujustdividetheoffavouriteblowoutcomesbythetotalnumberofpossibleoutcomesokay
imaginerollingasixciteddieeokay
whatstheprobabilityofrollinginevennumberletsseetherearethreeevennumbers
yeah
twofourandsixatsixtotalpossibilitiessothreevidedbysixgivesusafiftypercenenttion
exactlyyoujustcalculateabasicprobability
yes no
whataboutcardsok
whatstheprobabilityilitydrarawingandacefromastandarddeck
therearefouracesandfiftytwocardstotalsosodividedafiftytwogivecuus
youknow
youknowadviaAAAababgivesussowhataboutcardslessthanonetenthokay
soroughlyaroundeightpercentgotit
sofarsogood
yeah
butwhataboutwhenthingsgetmorecomplex
whatif
ifwannaknowtheabability
rollingsayasixorafive
thatswhereweintroducedthelawofunionsokay
whichisfindtheprobabilityofatleastoneoftwoeventshappeningokay
weaddtheprobabilitiesoflaveunionsokay
andthensubtracttheprobabilityofbotheventshappeningokay
walkmethroughthissowiththediceexampleokay
theprobabilityofrolling
six
sixissixteen
theprobablyrollingoffive
yes
alsosixteenokay
weaddthosetogether
whichgivesustwentysixokayoronethird
onethirdgotit
butthenwehavetoconsidercanwerollbothafiveandasixatthesametimewithoneeye
noimpossible
exactly
sotheprobabilityofrollingbothoffiveandasixatthesametimeiszeroright
sowesubtractzerofromthirteenokay
whichleadsuswithathirtychanceokayoraboutthirtythreepercentgotitsoyouseeallthatworks
yeah
youreaddthosepossibilitiestogetherright
butyouretakingawaytheoverlaprightbecauseitcanthappenok
ayahletstryanotheroneokay
tstsdowhatstheabilityilitydrarawingfacecdsorspadeooayfromadeckofcards
ohay
thisisinteted
nowthisiswhereweneedtobecarefulnottodoublecountokyeahwehavetwelvefacecardsandthirteencardsright
butsomecardsarebothrightright
soifwesimplyaddtheprobabilitiestogether
yeahwerecountingthejailqueenandkingofspadadtwtwicerightsohowdoweadjustforthatwellwe
sowehadtheprobabilityofafacecardtwelvefiftytwookay
totheprobabilityofaspadethirteenfiftytwookay
thatgivesustwentyfive
fivefiftytwo
thenwesutracttheprobabilityofgettingafacecard
thatisalsoaspadeokay
thatsthreefiftytwo
yeahahlelesuswithtwenty
twentyfiftyperco
thenlittleoverfortytwopercentokay
imstartingtosee
howtheseseeseeinginglymplecalcucutionoyeahcangetprettytricky
theycan
andthatswhyunderstandingtheunderlyingcepceplikethethewofunionsiskey
yeah
exactlynowimagine
youknowflippingacoinokay
theoutcomeofonememory
yeah
doesntinfluencethenext
thesearewhatwecallindependentevents
soevenifigetten
tenhesinarow
yes
thechancesofgettingtaesonthenextflip
itsstillfiftyfifty
heresstillfifty
fifty
exactly
thecoindoesntrememberyeah
doesnthaveamemoryright
eachflipisafreshstartmakesenseand对对对
tofigureout
theprobabilityofmultipleindependenteventokay
happeninginasequenceyeahweusewhatscalledmultipleiclamumultipliclawsoundscomplicatednosoreallylittlelikethisokay
eachindependentevent
oh
asanotherlayerofimprobabilityokay
sothechancesoftwounlikelythingshappeninginarow
yeah
getreally
itreallyfast
oh
thatsagoodwaytothinkaboutit
yeah
sotheprobabilityofgettingno
twoadadsinarowforexamplewouldbetwelvetimes
twelvetheequals
fourteen
teenyougotitokay
andtheprobabilityofgettingthreeheadsinarow
rightwouldbetwelvetimes
twelvetimestwelverightoreighteenokay
thatmakesthat
thatssook
thatwhataboutsituations
whereoneofitdoesinfluencethenext
thatswhatwecalldependenteventsok
andthatbringsustotheconceptofconditionalprobabilityokay
theprobabilityofsomethinghappeninggiventhatsomethingelsealreadyoccurredokay
imagineabaggwithfiveredmarblesokay
andfivebluemarblesokay
youdrawonemarbleanditsredokay
youdontputitbackinokay
nowwhatstheprobabilityofdrawinganotherredmarble
wellnowthereareonlyfourredmarblesleftleareoutofatotalofninemarblesexactly
sotheprobabilitywouldbefortynineacactlyokthefirsteventdrawingaredmarble
andnotreplacingitrightchangetheconditionsforthesecondeventokay
cool
sofarwevebeentalkingaboutprobabilitieswithyouknowclearlydefinedoutcomeslikewithcardsordiceright
yeah
butwhataboutthings
thataremoreuncertain
wherewedonthavealltheinformation
thatsagreatquestion
thats
wheresubjectiveprobabilitycomesinokay
andthisiswheregegetsyouknowalittlebitmoreintotherealmofpsychologyandhumandmentookitsyourpersonalestimate
yeah
howlikelysomethingisokaybasedonyourknowledgeandexperience
icanseehowthatcouldbeprettydifferentfromperson
aperson
itabsolutelyisright
itabsolutelyisthinkabouttwopeopleassessingwhetherlikeaparticularstockok
going
going go
gouptomrowright
theyresubjecttiveababilitytiesdifferdrasticallybasedontheirunderstandingofthemarketrightandsubtlessotherfactorokay
so是的
我的这个
howcanwegaugeifsomeonesubjectiveprobabilityyetactuallyaccuraterightistherewaytotestitthereiscool
exeldescribessomethingcalledthedefinitygameokay
whichrevealssomeonestruesubjectiveprobabilityokbyconsideringthebets
theybewillingtotakeinterestingtellmemoreaboutthisgame
是的 对的
是有那个
soimagine
askingsomewhatabouttheprobabilityofraintomorrowok
insteadofjustgettingapercentageright
yeah
youofferthemaseriesofbetswithvaryingamountsandoddsokay
soyousaywouldyoubettendollarstowinfiftydollars
ifitrainsins
wouldyoubetfiftydollarstowintendollars
oh wow ok
andbyanalyzingtheirchoices
嗯 有没有
youknowyoucangetabettersense
yeah
theyretruebelief
wow
thatsreallycleverisntitcool
yeah
itforcedpeopletoputtheirmoney
wheretheirmouthisitdoesevenifitsjustyythetheal
exactlyitcutsthroughtheanswertyandreveals
yeah
howtheyreallyfeeliloveit
youshouldtryoutwithyourfriendsyeah
itsfuntoplayaroundwithiwillokay
nowtheresanotherconceptfromthebook
iwanttotouchon
andthatisthecomplimentofaneventokay
sothecomplimentissimplytheeventokay
nothappenokay
gotooahahnowtheeventisitwillraintomorrow
yeah
thecomlimentisitwillnotraintomorrow
seemsprettystraightforwarditiswhyisthisimportant
because
becausetheprobabilityofaneventhappeningokay
plustheprobabilityofitscomlimenthappeningalwaysequalsonehundredpercentokay
rightsoiftheresathirtypercentchanceofraintomorrowright
theresaseventypercentchance
itwillnotraingotitoneortheotherhastohappenpreciselyokay
thatandthatleadsustoaconcept
yeah
thecowcallsthelawunionsofindependenteventsokay
andthisone
thisonehelpsuscalculatetheprobabilityofatleastyeahofseveralinpendenteventsoccurringokay
sohowdoesthisworkyeah
imallaboutthepracticalapplications
hereisosoimagineyouapplyingforfivejobsokay
eachwithatwentypercentchanceofgettingitofferright
是的 是的
nowyoumightfeeldiscouragebythoseindividualliyes
yeah
buttheloveunionshelpsusseethebiggerpictureoksohowdowecalculateateoverallprobabilityofgettingatleastonejobofferright
dowejust
dowejustaddthosetheababtiestogethernotquookayactuallylookattheprobabilityilityofnoneoftheeventhappenoohkayright
sointhiscase
eachjobhasaneightypercentchanceofnotresultinginanofferrightsowemultiplyeightyperentbyitselffivetimerightrepresentingeachjobapplicationokay
andthisgivesusaboutthreethreepercentokay
soifwesubtractthatfromahundredpercent
wegetasixtysevenpercentchanceofgettingatleastonejobofferthatssurprisinglyhigh
itkitsagoodreminder
thatevenwhenindividualevorunlikelyrightpersistencecanpayoffabsolutely
andthislawisntjustaboutjobhuntingokay
excelgivesusaverysimilarexampleokayumawomangoingonjojobtingtesookaytheindivilawprobabilityoffindingyouknowagoodmatchoneachdayrightmightbelowyeah
buttheoverallprobabilityofsuccessismuchhigher
whenyouconsiderallfivedatestogetherokay
thatsstartingtomakealotmoresensegood
itseemslikeourinfitiontionaboutprobabilitycanbeprettyunreliable
youreabsolutelyrightright
andthatbringsthistothestoryofthiscivleiademarayokay
agamblerwhohadsomerightstronghunchesokay
abouttheoddsintwodifferentdaysgamesokay
butintuitionledhimmistray
ohoh
andhisexperienceactuallyendedupsparkingthedevelopmentofmodernprobabilitytheoryokay
imallyearswhatwerethesegames
andhowdoyougetitwrong
sothefirstgameokay
involvedrollingasingleeyefourtimesokay
andbettingonatleastonesixcomingupokay
nowdemrefiguredhehadatwentythreechanceofwinningokay
sincetheprobabilityofrulinglingsixthanyanygivenroleissixteenright
andhewasrollingfourtimes
thatsoundslogicalenough
itdoesrightyeah
butitnsoutouthisintuitionactuallyunrestimatedhischancesokay
hewaswinningyeah
youknowthisgamemoreoften
sohisgoodtwothirdsofthetime
sohesgoodfeelingwasoff
我二一二一
一一二零的一的
itwaswhatarethesecondgame
thesecondgameinvolvesrollingtwodicetwentyfourtimesokay
andbettingonatleastonedoublesixappearingokay
hethoughtthisgameyouknowusingthesamelogicyeah
alsoalsohaveatwentythreechanceofwinning
but
butheacactuallywinninglessthanhalfthetime
oh
rightso
sothistime
sothistime
hisintuitionoverestimatedhischancesofwinning
exactlysohewasreally
reallyyeah
hecouldntfigureoutyeah
whyhishunchesdidntmatchrealityyeah
andthatswherebacedpascalcomesinokay
imbrilliantmathematitionokay
enreststhepicturesopassgalmusthavebeenabletoexplainwhatwasgoingonpascal
usingwhatwevenowcallyouknowthelawunions
right
youknowtheveofuseofindependenteventscalculatedtheactualprobabilitiesforeachgameokay
anditturnsout
theprobabilityofwinning
thefirstgamewasslightlyoverfiftyonepercentokay
whiletheprobabilityofwinning
thesecondgamewasalittleunderfortyninepercent
wow
sodemiysintuitionwaswronginbothcasesiknow
butinoppositedirection
exactlythats
whileit
itissoevenaseasongamblercangettrippedupyeah
byprobabilitytheycan
inthechivoliidemerrousstoryisjustthebeginningwereabouttodiveintosomeyouknowevendeeperconceptslikerandomwalksthegambersruinandthesurprisingways
youknowchanceshapesourlivesimready
alright
letsgolegotodivetoourdeep
diveintoprobabilityokay
beforewewentdeeper
weweretalkingabouthoweventheseasongambersersknowcangivefuoolbyininterlutionsaboutchancetollysonowweregoingtoexploreaconceptcalledrandomwalks
randomwalkitsoundsmorelake
youknowastrawlingcontheparkandlikeamathematicicalconcept
itmightsoundpoeticoouhapowerfulidea
okay
soannotinstepforward
okay
foreachheadsyoutakestesteforwardard
okforeachtails
youtakeastepbackok
thepathewtracethatsrandomwalk
okay
ilikeit
yeah
soitslikeavisualrepresentationofpurechance
likeyoucoulddnthavegoingforwardbackward
justjustkindofzexagandaroundexactlyandheres
whereitgetsinterestingokay
evenwithafifty
fiftychanceoneachcoinflipyourerekelylyseeseestreetsofsteps
youknowinonedirectionortheotherokay
right
wetendtothinkthatrandomeventsshouldevenoutquicklyright
yeah
butthatsnotalwaysthecase
soeventhougheachindividualstepisrandomright
theoverallpathcanhavetheseunexpectedlikerunsofluck
yes
whatdoesthistellusaboutsaylikegambling
ithashugeimplicationsforgamblers
okay
thispatternhelpsexplainwhyevenwithdecentoddslikeonindividualbets
gamblersarekekelytolosethemalongrunespeciallyagainstthecasinoisyouahthosebuilbuilinadvantage
soeven
ifyouwinsomebetshereandthere
yeah
thoselonglosingstreetscanreallysetyouback
youcanitalmostfeelsliketherandomness
itselfisworkingagainstyou
itsnotthattherandomnessssyouknowokay
intentionallymilaliciousright
butthoselonglosingstreetsaremorecommon
yeah
thanourintuitiontellsusokay
andtheresaum
theresamathematicaltheumokay
callthegamblersruintheoumgamblersruintheorethatsoundsominousyeah
itessentiallysaysthatifyoukeepgamblingyeahagainstunopponentwithmoreresources
yeyourmathematicallycertaintoloseeverything
eventually
soifyourelikeplayingagainstthehousesingcasino
whichhaswayweperpocketsthanyoudoyestheodersstackedagainstahfromthestart
fromthestartyeah
exactlyitsasobberingreminderthatyouknow
evenifyouhavelikealuckystreakearlyonthelongeryouplayright
themorelikelyyouaretohitthatlosingstreets
lilifesweoutsoknowingthisarethereanylakesmartstrategiesforgamblers
orisitjustallamatteroflikepingingthethebacktheresnoguaranteepasttoricbers
butthere
thereareapproachesthatareyeah
theothersokay
soexcelgivesthisexampleofsomewhoneedstoturntwentythousanddollarsokayintofortythousanddollarsokay
hadarelativeok
okay
whatwouldyoudo
inthatsituationumithinkiprobablytrytoplayitsafeyeah
youknowmakingsmallbetstominimizemylosses
itseemslikethatwouldgivemethebestchanceofyouknow
slowlyyeah
ahworkinmywayuptomycalthatswhatintuitiontionmyllesateyeah
but
butinthisspecificscenario
yeah
aborderapproach
whereyouriskalargeramount
itwantsokayactuallyhasahigherprobability
ittingthetargetyeah
thatyoullcouncountingtoit
iknowwhyisthatsotheresatradedeoffright
cautiousplayright
mightfeelsaferright
butittakesalotlongertoreachyourgoalgivingthoserandomfluctuations
moretimetoworkagainstyouokay
rightsowithboldplayyeah
youeitherwinningbigquicklyorlosingquicklyyeah
lesstimeforthosestreekstodevelopboldplayisundeniablyriskyyeah
butitoffersabetterbigskirtatreachingyeah
thatsspecifictargetamountokay
thatsinterestingokay
soletssaylikefeelinglucky
andonchiisbowlapproach
rightis
istheclassicdoublingstrategy
agoodidea
youknowwhereyoudoubleyourbedaftereveryloss
sothatwhenyoufinallywinyourheadyeah
itseemslikethatwouldlikeguaranteewineventuallyitsaverytemptingstrategy
buttheresafatalflawyeah
remberthoselosingstrikes
kstalkaboutyeah
yeah
allongenoughlosingstreakcanwipeyououtrightbeforeyouhaveachancetorecoverrightokay
and and
andaswediscussedyeah
gienenoughtimethoseincrediblyunlikelyeventsbecomealmostuninevitable
soeveniftheoddsoflosingsayliketentimesinarowyeah
areauteromicallyyeah
itsnotimpossible
itsnotimpossible
andifthathappenedyourefinishedexactlyokay
andthats
whythedoublingstrategywhileappealingonthesurfaceaceisultimatelyunsustainable
sothelessonhereisyeah
donttrythisathomeoratthecasino
yeah
dontdoit
是的 对的
buttheseideasoflikerandomwalksandprobabilityrightgofarbeyondgamblingwereabsolutelyrightyeah
exelshowshowtheseconceptsapplitoallsortsofthingsokay
youknowhetalksabouthowrandomwalksandarelatedconceptcalledbrownieandmotionareusedtouhmodeltheopsanddownofthestockmarket
是的 对的
soeventhoughtheremightbelikelongtermeconomictrends
likeonadateddaybasis
alotofthestockmarketsmovement
rightisessentiallyrandom
thats
thatsoneinterpretation
yeah
andthatswhyyeah
tryingtopredictshorttermstockmovementyeahcanbeafuooseerrenright
rightok
thatmakesmewonderaboutrandom
ititselfyeah
andwhatdoesitevenmeanforsomethingtobetrulyrandom
thatsa
thatsaprofoundquestion
yeisrightxwellahuseagreatexampleokayimaginewalkingintoabar
rightok
andseeinghowpeopleareseatednowourbrainsare
arewiredtospotpatternyeah
sowecanusuallytellintuitivelyokaythearrangegementlooksrandomarenot
soifweseelikesayallthewomensittingononesideofthebaryeah
andallthemenontheotherwebelikethatdoesntntveryrandom
exactly
but
buthereswhereitstrickynotpeerranceouessdoesntnecessarilycreateperfectlyevendistribuyeahitsentirelypossibletohaveclutchresstreeksyeah
appearevenincompletelyrandomdata
sothoseseeminglylikenonrandomstreeks
wetalkedaboutinrandomwalk
yes
thoseareactuallyanormalpartofrandom
nessitselfprecisely
wow right
andthishasbigbigimicicyesforhowweinterpreteventsinourownlivesyeah
wehas
hasastrinksofgoodluckyeahorbadluck
weahwethingsbigimplthree
ahandwethinktheremustbeapattern
yeah
yeacahahah
yeah
thesearejusttheresultsofrandomstplayingoutovertime
sothatlikeluckystorygununfeelingtodaymightjustbelikeastatisticalblipyeah
notasignthativesuddenlybecomeamagnetforgoodforununit
itcanahumblingthoughtisinit
itisyeah
ourbrainscravepatternsandmeaning
butsometimesyoucanreallyjustjusthaverightandspeakingofpatterns
youknowXLintroducesesustothisreallycoolvisualtool
okay
theycanhelpunderstandtheseideasbetterandcalledptticlestriangle
pascels
triangleyeah
ivaglyrememberthisyeah
fromhighhighschool
matclclwasntitsomethingaboutlikeapymidofnumbers
thatsitkthisthisarranrangementofnumbers
whereeachnumberisitsthesumokayofthetwonumberyeah
directlyaboutitokay
andwhatmakesitsofascinatingisitsconnectiontoprobabilityokay
imofficiallyintriedwhatstheconnection
itshowsustheprobabiliofofwhatstheconnectioninuhaseriesofcoinflipsokayoranyeventreallytwoequallylikelypossibilities
soififlipacoinlikefivetimesyespasscalestrianglecantellmetheprobabilityofgettingthreeheadsandtwotail
exactly
anditalsorevealsasurprisingfactiskisyeah
asthenumberofquintosses
increasestheprobabilityofgettinganexactlyevensplitofheadandinactuallydecreases
soififlipacoinlikeathousandtimes
yesitsmuchlesslikelytobeaperfectlesslikelyfivehundredheads
fivehundredtailspspt
yesyes
thenonlyonlyflipattimesexactly
yeah
itsoneofthosethings
wow
thatsreallycounterintuitiveisntityeah
itseemslikeyouknowmoreweflipthecoinyeah
thecloserwhichshouldgetyeahtoafiftyfiftysplitright
butthemathsaysotherwise
themathsaysotherwiseits
itsfunnyhouse
oftenyeah
thisremindsmeoflikehowwetalkedaboutintuitions
leadingisastraightreallyyouyourecatchingrightandthisleadsustoanotherfascinatingparadox
ookaythatexceldiscusessesokay
theinspectionparadox
theinspectionparadoxokimreadyforthisoneright
sothinkaboutalightbuboright
thatsbpostthelastoneaveragetwothousandhoursokay
youhaveonethatsbeenburningforoverayearokay
itseemslikeitslikedefyingtheoddsright
itdoesright
ahsotheinspectionparadoxis
isthatsodedeingtheodcessrightrandomtimeokay
weremorelikelytofindourselvesyenolongerthanaveragegeneralokay
whichkindofyouknowyeah
skilseareperceptionokay
canyouexplainthatalittlemoreyeah
imnotsure
imimtotallyfollowingsoimagineabunchoflightbulbokaysomewithshortlightspansyeah
andsomewithreallylongonceokay
ifyoupickalightbulbatrandom
yes
andyoucheckhowlongitsbeenburningyeah
youremorelikelytoselectonethatsbeenrunningforawhile
oh okay
causetheresmoretimetolikecatchitexactduringoneofthoselongerintervals
theyremorelikelyfindine
ahahinoneofthoselongerintervalsokay
soitsnotthatthelightboldismagicalordefyingtheodgs
yes
itsjustthatourmethodofobservationrightismakingitseenthatway
wowthatswhileright
andthissuppliestoothersituationstoolikelikewaitingforbuses
ohsothebusisalwayslate
itfeelsthatwayrightitsreallydoesyeallyyouremorelikelyatarrivevethethebusstoppuringuringlongerinterval
betwtwebusesokay
whichmakesitseemlikethebusisconsttlyrunningbehindscheduleokay
thisismakingmequestion
ithing
ithought
iknewabouttheworldrightarethereanyothersituations
wherelikeexcelappliesthisheevenusesityeah
toexplainwhypeopleoftenlivelongerokay
thentheaveragelifespanfortheir
theirdemographic
anditsbecausetheyvealreadysurvivecertainrisks
thatothershaventtheyvemadeitpastthoseyeah
shorterintervalssotospeak
sososimplybybeingaliveandhealthyatacertainageyeah
yourealreadylikebeatingtheaverageinaway
yeah yeah
butuhlets
letsmoveontoyeah
AAclassicprobabilitypuzzle
thatthatofstustumppeopleokay
ahthebirthday
thebirbirdayproblem
problem
you
youheardthisone
iveheardardthisone
yeah
ahkayitsabouthowyouneedsurprisinglyfewpeopleyeah
haveagoodchanceyeah
tooimsharingabirthday
yeah
ahyougotitokay
sowithjusttwentythreepeopleinaroomokay
theresagreaterfiftyperperententchyeahoftwoofthemsharingabirthday
yethreepthats
thatswaylowerthaniwouldgetguestourbrainstendtofocusonyeah
matchingaspecificbirthdayright
youknowyourbirthdayrightratherthananytwobirthdayswithinthegroup
isaysowere
sowerekindofoverlookingalltheotherpossibleparentexactlyrightokay
righthighlightswhatagecleyeah
thepowerofaggregationokay
evenwiththreehundredsixtyfivepossiblebirthdaysyeah
thoserandomoverlapshappenedmorefrequentlythanweexpectrightandtomakeitevenmoreinterestingyeah
thereare
thereareformulastocalculatethisprobabilityokayforothercategoriestoookay
youknowlikewhataretheawdsoftwopeopleinaroom
yehavingthethebirthweekrightrightorthesamebirthdayinprofession
soitsnotjustwhathavebrouerapplicationitdoesactuallyhelpsexplainthesurprisingfrequencyofcoincidcesinourlives
nowiretalkingcoincidces
iknowrighteveryonelowsagoodcoincidencestorysoexlyeahsharesuhacompellinganecdoteactuallyokayaboutaseriesofcoincidces
heexperiencededvovovinghiswifeokay
anditsbookeditorum
ohwow
impicturinglikeascenestraightoutofamovie
itsthatgoodokay
anditmadehimrealizeyeah
thatthoseseeminglyimpossiblecoincidencesareactuallymuchmoreprobableyeah
thatwethinkjustlikethebirthdayproblem
soitsnotthatcoincidencearelikemaketobeorwhateveritsjustthattherearesomanypossibleconnectionsouttherearelikeoveroverlapsareboundtohappenexactlyandcertainfactorslikebelongingtoyeah
youknowspecificnetworks
groups
yeah
canincreasetheprobabilityofthoseoverlaps
oahexextaltaltalksaboutahright
嗯flyfrequentlyrightaremorelikelytoexperiencecoincidencesyeah
simplybecauseyeah
theyreinteractingwithalargerpoolofpeoplethatmakesenseyeah
rightitsits
itssimilartotheideaofyouknowsixdegreesofseparation
rightyoureallconnectedyeah
ofweoftendontalializelovethatitmakesthoselikechanceencounterersevenevenmorespecial
andknowingthatthereyeah
theresultofthislikecomplexwebofyeconactionprobability
andithighlightsyeah
howmuchwestilldontknowaboutthe
theinterplayofofrandomnessandpatternsnsour
ourlivesrightbutlets
letsmoveontooneofthemostpracticalapplicationsofprobability
okay
andthatismakingdecision
oh okay
thisiswherethingsgetalalright
becauseweallfacethesebigdecisions
wherewedonthaveperfectinformationright
howcanprobabilitytothisinthosesituationsintroducesustoastrategy
okay
callthethirtysevenpercentruleokay
thirtysevenpercent
thirtysevenpercent
right
itsthisitsthismathematicallyprovenwayokay
tomaximizeyourchansofindingthebestopopokay
whenyourealimitednumberofchoices
right
andyoucantgobackahonceyouvemadeadecision
ok okay ok
imintreat
howdoesitwork
somamagineyourlookingforanewapartment
okay okay
youplantolookatahundredlistings
okay
嗯accordingtothethirtysevenpercentrule
youshouldcarefullyevaluatethefirstthirtysevenlistingsokay
withoutmakinganyoffersokay
thenyoupicktheverynextdepartment
okay
thatsbetterthanalltheonesyouseeenbefore
soyoureessentiallylikeusingthatfirstthirtysevenpercentaslikeacalibrationperiod
exactlyrightrightitmightfeelcounterintoit
itbecauseyoumightworryaboutyouknowmissingoutonsomethingbetteryeah
ifyoustoplookingtoosoonyeah
exactlyyeah
butmathematicallyyeah
thisstrategygivesyouthehighestprobability
okoffindingthebestoption
itslikefindingthatsweetspotbetweenlikeyeahgatheringenoughinformation
rightandnotlettingliketheperfectopportunityslipaway
thats
thatsagreatwaytoputit
andthisruleisntlimitedtoapermanentofcourseinapplutoyouimallsortsofyeah
bigdecisionsfromfromchoosingajobtofindingalifepartnerokay
right
imdefinitelygoingtotry
trytorememberthisthirtysevenrule
raahyeah
itsagoodonefefeelslikeyouknowsecretweapon
yeah
werenavigatingthose
thosebiglifealteringchoices
butwerenotdone
yettherearestillafewmoreconceptsfromthebooktoexploreincludingbasasetheumandthenormalcurveletsdoitwelcomebacktoourfinalsegmentofthisprobabilitydeepdive
yeah
wevebeenexploringsomeminebendingconcepts
andnowitweregoingtodiveintosomelikepowerfultoolsthatexelldescribesincludingbetheumumokandthenormalcurvereadyfrommorefastcatinginsights
tsabsolutelysobasasetheroomokay
despitethelikeintimidatingmayorisallaboutupdatingourbeliefsokay
aswegetnewevidenceokay
updourourbeliefbasedonnewevidence
ithinkidothateverytimeichecktheweatherappyouprobablydoright
yeah
givemeanexampleofbasethereuminaction
okay
letssayumtheresresmeddicalforararedisease
okay
thatsaninetyfivepercentaccurateokay
ifyouweregettingtestedhowconfident
wouldyoufeelontheresult
ifthetestisninetyfivepercentaccurate
ididfeelprettyconfident
thats
thatsareasonablereact
yeah yeah
but
butbasediummkind
kindremindsus
ustoconsiderotherfactorstoookay
know
knoweventhatthataccuracy
okay
apositiveresultyeah
mightnotactuallymeanyouhavethediseasereedainitsohowisuppossiblesobasedthemsaysweneedtoalsofactorinokay
howcomeonthediseaseesyeah
yeah
rightif
ifthediseaseisveryrare
okay
thechancesofalikefalsepositiveoractuallyhihiredthanyoumightthinksosoitsnot
notjustabouthowgoodpetestisitsalsoabouthowlikelyyouareexactlyaconditioninthefirstplay
exkaythisistheomhelpsuscalability
youknowthetrueprobability
yeah
byconsideringboththetestresultandthoughlikepriorprobabilitywiththatbaselinelikelihood
yeah
itsaboutcombinnewinformationwithwhatwhatareweknow
okay
thisisstartingtomakesense
itslikeputtingthetestresultsintocontextexactlyandanxlillustratesthiswithlikeaclassicthoughtexperiment
okay
theprisonerproblem
theprisonerproblem
thatsoundslikekindofdramatic
soimaginethreeprisonersinacell
okay
oneofwhomisgoingtoexexetedookoneprisonerasksthewarden
yeahtoapointtooneoftheotherprisonerswhowillnotbeexecuted
ok right
doyouthinkthisnewinformationchangeshischancesofbeing
theonewhosexecute
itseemslikeitwouldincreaseschances
itdoesbecausenowitslikeaahfifty
fifty
fiftyicebetwtwenenhimandthe
andtheremainingprisoner
yeah thats
thats
ourintuitionmighttellusright
butthistheremshowsusthathisprobabilityofbeingexecutedactuallystaysthesamewhatyeahitsstilloneoutofthree
wow
thatsrealheadadratcher对不对
对对
isntit
itseemslikethenewinformationshouldchangetheodds
butitdoesntincrediblycounterintuitivetoityouknowbasasetheremhelpsuskindofunravltheseseeminglyparadoxicicalsituationsright
rightandspeakingofthingsthatshowupanunexpectedacuyeahletstalkaboutthenormalcurve
okay
thenormalcurve
itsthethefamousbelcurveright
iveseenitinlikecountlessgraphsandcharts
andwhatnotwhatsthebigdealaboutit
itsoneofthemostfundamentalconceptsinyouknowprobabilityandstatisticsokay
youknowthethe
thebelshapeappearsinlikeavasterayofnaturalphenomenonokayyouknowfromhumanheightandwaittostockpricestoexamscores
soitsnotjustlikesomerandomshape
itsareflectionofhowthingsactuallydistributeintherealworldexactly
andbecauseitspovertiesaresowellunderstoodright
wecanuseittocalculateprobabilities
yes
foranythingitfollowsthispatternforexample
allyaboutsixtyeightpercentofthedatawillfallwithinonestandarddeviationofthemean
okayaboutninetyfivepercentwillfallwithintwostandarddeviations
soifiknowthatsomethingfollowsanormaldistribution
likeicanmakesomeprettysolidpredictionsaboutwherethedatapointsaregoingtofall
exactly
andthosepredictionsareincrediblypowerful
yeah
itfeelslikefinancemedicinerightandevenpupollingspeakingofpolls
yes
ibetthenormalcurveiskeytounderstandinglikethosemarginsoferrorrightspopoon
oh yeah
soXLexplainshowthesultstsrandompols
yeah
alsofollowanornormaldistributioncentrearound
youknowthetruepopulationvalueokay
andthatmarginofair
yeah
thatreflexiuncertaintyinherentinausingasample
yeah
youknowtorepresentthewholepopulationokay
sowhenapolesaysthatyouknowacandidatehaslikeafiftyfivepercentsupport
嗯yeahitlikethreepercentmarginofar
yeah
whatdoesthatactuallymean
itmeansyoureninetyfivepercentconfidencethatthetruelevelofsupportforthatcanadafallssomewherebetweenfiftytwopercentandfiftyeightpercent
okay
thisisallstartingaclicknowyerightitslikethoseseeminglylikeabstractmathconceptsaresuddenlythoseseeingalivegoodwhatanrealworldapplicationandthatdearlistener
yeahbringsustotheendofourexplorationofprobability
whatanincrediblejourney
itsbeen
ithasbeen
wevelearnedhowameasureprobabilitywevegrappledwiththosemindbendingparadoxes
yesweveexplloredhowchanceshapesyouknowourdecisions
ourperceptions
itdoesandevenourlivessoexileleavesuswithonefinalthoughttoponderokayppureandomessleadstomoreclustersandpatterns
thatwemightexpect
yeah
howmightdisaffectourunderstandsofseeminglyorganizedpatterns
thatwemightexpeusthatsaprofoundquesinethislekisfindsustobelikebothcuriousandsceptical
yestotoalwaysquestion
ourassumptionrightandtobeopentolikethesurprisingways
chanceoperatesinourlives
ihopeyouveenjoythisdeepdiveintotheworldofprobability
yeahrememberevenabasicunderstandingoftheseconcepts
yeahcanreallyempoweryoutomakebetterdecisionsrightandseetheworldwithAAfreshperspectivetotallyuntilnexttimedeepdivers
yesstaycurious
keepexploring
nevertilustomeetthepowerofchance
