{"id":1345,"date":"2023-07-26T19:12:25","date_gmt":"2023-07-26T19:12:25","guid":{"rendered":"https:\/\/statorials.org\/tr\/en-az-bir-basari-olasiligi\/"},"modified":"2023-07-26T19:12:25","modified_gmt":"2023-07-26T19:12:25","slug":"en-az-bir-basari-olasiligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/en-az-bir-basari-olasiligi\/","title":{"rendered":"En az birinin olas\u0131l\u0131\u011f\u0131 nas\u0131l bulunur? ba\u015far\u0131"},"content":{"rendered":"

<\/p>\n

\n

Olas\u0131l\u0131k<\/strong> bize bir olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n ne kadar oldu\u011funu s\u00f6yler.<\/span><\/p>\n

\u00d6rne\u011fin, belirli bir okuldaki t\u00fcm \u00f6\u011frencilerin %4’\u00fcn\u00fcn en sevdikleri ders olarak matemati\u011fi tercih etti\u011fini varsayal\u0131m. Bir \u00f6\u011frenciyi rastgele se\u00e7ersek matemati\u011fi tercih etme olas\u0131l\u0131\u011f\u0131 %4 olacakt\u0131r.<\/span><\/p>\n

Ancak \u00e7o\u011fu zaman birden fazla<\/em> denemeyi i\u00e7eren olas\u0131l\u0131klarla ilgileniyoruz. \u00d6rne\u011fin \u00fc\u00e7 \u00f6\u011frenciyi rastgele se\u00e7ersek, i\u00e7lerinden en az birinin<\/strong> matemati\u011fi tercih etme olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n

Bu soruyu cevaplamak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullanabiliriz:<\/span><\/p>\n

1. Bir \u00f6\u011frencinin matemati\u011fi tercih etme olas\u0131l\u0131\u011f\u0131n\u0131 bulun.<\/strong><\/span><\/p>\n

Bir \u00f6\u011frencinin matemati\u011fi tercih etme olas\u0131l\u0131\u011f\u0131n\u0131n P (matemati\u011fi tercih ediyor) = 0,04 oldu\u011funu biliyoruz.<\/span><\/p>\n

Dolay\u0131s\u0131yla bir \u00f6\u011frencinin matemati\u011fi tercih etmeme olas\u0131l\u0131\u011f\u0131 P(matemati\u011fi tercih etmiyor) = 0,96’d\u0131r.<\/span><\/p>\n

2. Se\u00e7ilen \u00f6\u011frencilerin tamam\u0131n\u0131n matemati\u011fi tercih etmeme olas\u0131l\u0131\u011f\u0131n\u0131 bulun.<\/strong><\/span><\/p>\n

Her \u00f6\u011frencinin matemati\u011fi tercih etme olas\u0131l\u0131\u011f\u0131 birbirinden ba\u011f\u0131ms\u0131z oldu\u011fundan, bireysel olas\u0131l\u0131klar\u0131 basit\u00e7e \u00e7arpabiliriz:<\/span><\/p>\n

P(t\u00fcm \u00f6\u011frenciler matemati\u011fi tercih etmez) = 0,96 * 0,96 * 0,96 = 0,8847.<\/span><\/p>\n

Bu, \u00fc\u00e7 \u00f6\u011frencinin en sevdikleri ders olarak matemati\u011fi tercih etmeme olas\u0131l\u0131\u011f\u0131n\u0131 temsil etmektedir.<\/span><\/p>\n

3. En az bir \u00f6\u011frencinin matemati\u011fi tercih etme olas\u0131l\u0131\u011f\u0131n\u0131 bulun.<\/strong><\/span><\/p>\n

Son olarak en az bir \u00f6\u011frencinin matemati\u011fi tercih etme olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n

P(en az biri matemati\u011fi tercih ediyor) = 1 \u2013 P(hepsi matemati\u011fi tercih etmiyor) = 1 \u2013 .8847 = .1153<\/strong> .<\/span><\/p>\n

Bir dizi denemede en az bir ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in a\u015fa\u011f\u0131daki genel form\u00fcl\u00fc kullanabilece\u011fimiz ortaya \u00e7\u0131kt\u0131:<\/span><\/p>\n

 P(at least one success) = 1 - P(failure in one trial) n<\/sup>\n<\/strong><\/pre>\n
 Yukar\u0131daki form\u00fclde n<\/em> toplam deneme say\u0131s\u0131n\u0131 temsil etmektedir.<\/span><\/p>\n
 \u00d6rne\u011fin, rastgele \u00fc\u00e7 ki\u015filik bir \u00f6rneklemdeki en az bir \u00f6\u011frencinin en sevdi\u011fi ders olarak matemati\u011fi tercih etme olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in bu form\u00fcl\u00fc kullanabilirdik:<\/span><\/p>\n
 P (en az bir \u00f6\u011frenci matemati\u011fi tercih ediyor) = 1 \u2013 (0,96) 3<\/sup> = 0,1153<\/strong> .<\/span><\/p>\n
 Bu, yukar\u0131daki \u00fc\u00e7 ad\u0131ml\u0131 s\u00fcreci kullanarak ald\u0131\u011f\u0131m\u0131z yan\u0131tla e\u015fle\u015fiyor.<\/span><\/p>\n
 “En az bir” ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in a\u015fa\u011f\u0131daki \u00f6rnekleri ek uygulama olarak kullan\u0131n.<\/span><\/p>\n
 \u0130lgili:<\/strong> “En Az \u0130ki” Ba\u015far\u0131 Olas\u0131l\u0131\u011f\u0131 Nas\u0131l Bulunur?<\/a><\/span><\/p>\n
 \u00d6rnek 1: Serbest at\u0131\u015f denemeleri<\/strong><\/span><\/h3>\n
 Mike serbest at\u0131\u015f denemelerinin %20’sini yap\u0131yor. E\u011fer 5 serbest at\u0131\u015f atarsa en az bir at\u0131\u015f yapma olas\u0131l\u0131\u011f\u0131n\u0131 bulun.<\/span><\/p>\n
 \u00c7\u00f6z\u00fcm:<\/strong><\/span><\/p>\n
    \n
  •  P(en az birini yapar) = 1 \u2013 P(belirli bir giri\u015fimi ka\u00e7\u0131r\u0131r) n<\/sup><\/span><\/li>\n
  •  P(en az bir tane yapar) = 1 \u2013 (0,80) 5<\/sup><\/span><\/li>\n
  •  P(en az bir tane yapar) = 0,672<\/span><\/li>\n<\/ul>\n
     Mike’\u0131n her be\u015f denemede en az bir serbest at\u0131\u015f kullanma olas\u0131l\u0131\u011f\u0131 0,672’dir<\/strong> .<\/span><\/p>\n
     \u00d6rnek 2: Widget’lar<\/strong><\/span><\/h3>\n
     Belirli bir fabrikada t\u00fcm aletlerin %2’si kusurludur. 10 adet aletten olu\u015fan rastgele bir \u00f6rnekten en az birinin kusurlu olma olas\u0131l\u0131\u011f\u0131n\u0131 belirleyin.<\/span><\/p>\n
     \u00c7\u00f6z\u00fcm:<\/strong><\/span><\/p>\n
      \n
    •  P (en az bir kusurlu) = 1 \u2013 P (verilen widget kusurlu de\u011fil) n<\/sup><\/span><\/li>\n
    •  P(en az bir kusurlu) = 1 \u2013 (0,98) 10<\/sup><\/span><\/li>\n
    •  P(en az bir kusurlu) = 0,183<\/span><\/li>\n<\/ul>\n
       10’luk rastgele bir \u00f6rneklemde en az bir par\u00e7ac\u0131\u011f\u0131n kusurlu olma olas\u0131l\u0131\u011f\u0131 0,183’t\u00fcr<\/strong> .<\/span><\/p>\n
       \u00d6rnek 3: Trivia sorular\u0131<\/strong><\/span><\/h3>\n
       Bob, \u00f6nemsiz sorular\u0131n %75’ini do\u011fru yan\u0131tl\u0131yor. Ona 3 \u00f6nemsiz soru sorarsak en az birine yanl\u0131\u015f cevap verme olas\u0131l\u0131\u011f\u0131n\u0131 bulun.<\/span><\/p>\n
       \u00c7\u00f6z\u00fcm:<\/strong><\/span><\/p>\n
        \n
      •  P(en az bir yanl\u0131\u015f) = 1 \u2013 P(verilen cevap do\u011frudur) n<\/sup><\/span><\/li>\n
      •  P (en az bir yanl\u0131\u015f) = 1 \u2013 (0,75) 3<\/sup><\/span><\/li>\n
      •  P (en az bir yanl\u0131\u015f) = 0,578<\/span><\/li>\n<\/ul>\n
         En az bir soruya yanl\u0131\u015f cevap verme olas\u0131l\u0131\u011f\u0131 0,578’dir<\/strong> .<\/span><\/p>\n
         Bonus: \u201cEn az bir\u201d olas\u0131l\u0131k hesaplay\u0131c\u0131s\u0131<\/strong><\/span><\/h3>\n
         Belirli bir denemedeki ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131na ve toplam deneme say\u0131s\u0131na ba\u011fl\u0131 olarak “en az bir” ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131 otomatik olarak bulmak i\u00e7in bu hesaplay\u0131c\u0131y\u0131 kullan\u0131n.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
        Olas\u0131l\u0131k bize bir olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n ne kadar oldu\u011funu s\u00f6yler. \u00d6rne\u011fin, belirli bir okuldaki t\u00fcm \u00f6\u011frencilerin %4’\u00fcn\u00fcn en sevdikleri ders olarak matemati\u011fi tercih etti\u011fini varsayal\u0131m. Bir \u00f6\u011frenciyi rastgele se\u00e7ersek matemati\u011fi tercih etme olas\u0131l\u0131\u011f\u0131 %4 olacakt\u0131r. Ancak \u00e7o\u011fu zaman birden fazla denemeyi i\u00e7eren olas\u0131l\u0131klarla ilgileniyoruz. \u00d6rne\u011fin \u00fc\u00e7 \u00f6\u011frenciyi rastgele se\u00e7ersek, i\u00e7lerinden en az birinin matemati\u011fi tercih […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1345","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n\u201cEn az bir\u201d ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 nas\u0131l bulunur?<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, belirli bir seride en az bir ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l bulunaca\u011f\u0131 \u00f6rneklerle a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/en-az-bir-basari-olasiligi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u201cEn az bir\u201d ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 nas\u0131l bulunur?\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde, belirli bir seride en az bir ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l bulunaca\u011f\u0131 \u00f6rneklerle a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/en-az-bir-basari-olasiligi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-26T19:12:25+00:00\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/en-az-bir-basari-olasiligi\/\",\"url\":\"https:\/\/statorials.org\/tr\/en-az-bir-basari-olasiligi\/\",\"name\":\"\u201cEn az bir\u201d ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 nas\u0131l bulunur?\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-26T19:12:25+00:00\",\"dateModified\":\"2023-07-26T19:12:25+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde, belirli bir seride en az bir ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l bulunaca\u011f\u0131 \u00f6rneklerle a\u00e7\u0131klanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/en-az-bir-basari-olasiligi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/en-az-bir-basari-olasiligi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/en-az-bir-basari-olasiligi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"En az birinin olas\u0131l\u0131\u011f\u0131 nas\u0131l bulunur? 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