Bir madeni para att\u0131n\u0131z ve \u00fcst \u00fcste be\u015f kez tura geldi. Sizce alt\u0131nc\u0131 at\u0131\u015fta yaz\u0131 gelme ihtimali art\u0131k daha m\u0131 y\u00fcksek? \u00c7o\u011fu insan i\u00e7g\u00fcd\u00fcsel olarak \u201cevet, art\u0131k yaz\u0131 gelmeli\u201d der \u2014 ve tam burada yan\u0131l\u0131r. Bu hataya istatistikte \u201ckumarbaz\u0131n yan\u0131lg\u0131s\u0131\u201d denir ve olas\u0131l\u0131k konusunda en s\u0131k d\u00fc\u015f\u00fclen tuzakt\u0131r. Bu yaz\u0131da bu yan\u0131lg\u0131y\u0131 ve do\u011fru d\u00fc\u015f\u00fcnme bi\u00e7imini ele al\u0131yoruz.<\/p>
Kumarbaz\u0131n yan\u0131lg\u0131s\u0131, ba\u011f\u0131ms\u0131z bir olay\u0131n ge\u00e7mi\u015f sonu\u00e7lar\u0131n\u0131n gelecekteki sonucu etkiledi\u011fini sanma hatas\u0131d\u0131r. \u201cUzun s\u00fcredir gelmedi, art\u0131k gelmesi gerekir\u201d veya tersine \u201cseri devam eder\u201d d\u00fc\u015f\u00fcncesi bu yan\u0131lg\u0131n\u0131n iki y\u00fcz\u00fcd\u00fcr. Oysa adil bir madeni paran\u0131n yaz\u0131 gelme olas\u0131l\u0131\u011f\u0131 her at\u0131\u015fta de\u011fi\u015fmez: her zaman y\u00fczde 50\u2019dir.<\/p>
\u0130nsan beyni \u00f6r\u00fcnt\u00fc aramaya programl\u0131d\u0131r ve \u201cdengenin sa\u011flanmas\u0131\u201d gerekti\u011fini hisseder. \u201cBe\u015f tura geldiyse, evrenin bunu yaz\u0131yla dengelemesi laz\u0131m\u201d gibi sezgisel ama yanl\u0131\u015f bir beklenti olu\u015fur. Ger\u00e7ekte madeni paran\u0131n haf\u0131zas\u0131 yoktur; \u00f6nceki at\u0131\u015flar\u0131 hat\u0131rlamaz. Her at\u0131\u015f, kendinden \u00f6ncekilerden tamamen ba\u011f\u0131ms\u0131z, s\u0131f\u0131rdan ba\u015flayan bir olayd\u0131r.<\/p>
Buradaki kritik ayr\u0131m \u015fudur: Madeni para, zar ve rulet \u00e7ark\u0131 gibi \u015feyler ba\u011f\u0131ms\u0131z<\/strong> olaylard\u0131r \u2014 ge\u00e7mi\u015f gelece\u011fi etkilemez. Ama bir desteden kart \u00e7ekmek ba\u011f\u0131ml\u0131<\/strong> bir olayd\u0131r: \u00e7ekti\u011finiz kart desteden eksildi\u011fi i\u00e7in sonraki olas\u0131l\u0131klar ger\u00e7ekten de\u011fi\u015fir. Yan\u0131lg\u0131dan kurtulman\u0131n yolu, kar\u015f\u0131n\u0131zdaki olay\u0131n hangi t\u00fcrden oldu\u011funu do\u011fru te\u015fhis etmektir.<\/p> Bu yan\u0131lg\u0131n\u0131n tarihteki en bilinen \u00f6rne\u011fi, 1913\u2019te bir rulet \u00e7ark\u0131nda topun arka arkaya 26 kez siyaha gelmesidir. Her turda \u201cart\u0131k k\u0131rm\u0131z\u0131 gelmeli\u201d diyen kalabal\u0131k, dengelenece\u011fi beklentisiyle b\u00fcy\u00fck kay\u0131plar verdi \u2014 oysa her d\u00f6n\u00fc\u015f hala ba\u011f\u0131ms\u0131zd\u0131. Kavram\u0131n matematiksel a\u00e7\u0131klamas\u0131n\u0131 derinle\u015ftirmek isteyenler i\u00e7in kumarbaz\u0131n yan\u0131lg\u0131s\u0131n\u0131n ayr\u0131nt\u0131l\u0131 a\u00e7\u0131klamas\u0131<\/a> iyi bir kaynakt\u0131r.<\/p> Olas\u0131l\u0131\u011f\u0131 ger\u00e7ekten anlayan biri, \u201cseri\u201dlere de\u011fil, tek tek olaylar\u0131n ger\u00e7ek olas\u0131l\u0131klar\u0131na bakar. Ge\u00e7mi\u015f sonu\u00e7lar\u0131 bir \u201cbor\u00e7\u201d gibi g\u00f6rmez. Bu disiplin sadece oyunlarda de\u011fil; yat\u0131r\u0131m, risk de\u011ferlendirme ve g\u00fcnl\u00fck karar verme gibi her alanda do\u011fru d\u00fc\u015f\u00fcnmenin temelidir. \u0130\u015fin hocas\u0131 olmak, sezginin yan\u0131ltt\u0131\u011f\u0131 yerde matemati\u011fe g\u00fcvenebilmektir.<\/p>","protected":false},"excerpt":{"rendered":" Bir madeni para att\u0131n\u0131z ve \u00fcst \u00fcste be\u015f kez tura geldi. Sizce alt\u0131nc\u0131 at\u0131\u015fta yaz\u0131 gelme ihtimali art\u0131k daha m\u0131 y\u00fcksek? \u00c7o\u011fu insan i\u00e7g\u00fcd\u00fcsel olarak \u201cevet, art\u0131k yaz\u0131 gelmeli\u201d der \u2014 ve tam burada yan\u0131l\u0131r. Bu hataya istatistikte \u201ckumarbaz\u0131n yan\u0131lg\u0131s\u0131\u201d denir ve olas\u0131l\u0131k konusunda en s\u0131k d\u00fc\u015f\u00fclen tuzakt\u0131r. Bu yaz\u0131da bu yan\u0131lg\u0131y\u0131 ve do\u011fru d\u00fc\u015f\u00fcnme … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-18","post","type-post","status-publish","format-standard","hentry","category-istatistik-olasilik"],"_links":{"self":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/18","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=18"}],"version-history":[{"count":1,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/18\/revisions"}],"predecessor-version":[{"id":19,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/18\/revisions\/19"}],"wp:attachment":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=18"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=18"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=18"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}En \u00fcnl\u00fc \u00f6rnek: 1913 Monte Carlo<\/h2>
\u0130\u015fin hocas\u0131 nas\u0131l d\u00fc\u015f\u00fcn\u00fcr?<\/h2>