Lihat solusinya<\/strong><\/div>\n<\/div>\n Pernyataan latihan memberi kita probabilitas berikut:<\/p>\n
A 1<\/sub> : Orang tersebut mengidap penyakit \u2192 P(A 1<\/sub> )=0,01
A 2<\/sub> : Orang tersebut tidak menderita penyakit \u2192 P(A 2<\/sub> )=0,99<\/p>\n B: Tesnya positif
B|A 1<\/sub> : Tesnya positif bila orang tersebut mengidap penyakit \u2192 P(B|A 1<\/sub> )=0,95
B|A 2<\/sub> : Hasil tes positif bila orang tersebut tidak mengidap penyakit \u2192 P(B|A 2<\/sub> )=1-0.90=0.10<\/p>\n Kemudian, untuk menghitung probabilitas bahwa seseorang yang dipilih secara acak benar-benar mengidap penyakit tersebut ketika dites positif, aturan Bayes harus diterapkan: <\/p>\n<\/p>\n
![\"P(A_i|B)=\\cfrac{P(B|A_i)\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c15e369635dcf17952b5d832a818d535_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
![\"P(A_1|B)=\\cfrac{P(B|A_1)\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d76df126cb6076aeba65aa7d1c12e344_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Jadi kami mengganti nilainya ke dalam rumus dan melakukan perhitungan probabilitas:<\/p>\n<\/p>\n
![\"\\begin{aligned}P(A_1|B)&=\\cfrac{P(B|A_1)\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-135e9ab7de6b44e7392fae0f5e70a125_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Singkatnya, kemungkinan seseorang yang dipilih secara acak dites positif dan benar-benar mengidap penyakit tersebut adalah 8,76%.<\/p>\n
<\/div>\n
Latihan 2<\/h3>\n
Diperkirakan peluang suatu saham naik dalam satu hari adalah 40%, stabil 10%, dan turun 50%. Lebih jauh lagi, kita tahu bahwa ketika pasar naik, ada kemungkinan 90% bahwa seorang analis keuangan akan memprediksinya dengan benar, ketika pasar tetap stabil, kemungkinan prediksinya benar adalah 75% dan jika terjadi penurunan, kemungkinan prediksi yang benar adalah 75%. 85%.%. Jika seorang analis memperkirakan bahwa pasar akan jatuh, seberapa besar kemungkinan pasar akan benar-benar jatuh? <\/p>\n
\n
Lihat solusinya<\/strong><\/div>\n<\/div>\n Dalam hal ini, pernyataan latihan memberi kita probabilitas berikut:<\/p>\n
A 1<\/sub> : Pasar naik dalam satu hari \u2192 P(A 1<\/sub> )=0,40
A 2<\/sub> : Pasar tetap stabil selama satu hari \u2192 P(A 2<\/sub> )=0,10
A 3<\/sub> : Pasar naik dalam satu hari \u2192 P(A 3<\/sub> )=0,50<\/p>\n B: Analis memperkirakan pasar akan jatuh
B|A 1<\/sub> : Analis memperkirakan dengan tepat bahwa pasar akan meningkat \u2192 P(B|A 1<\/sub> )=0.90
B|A 2<\/sub> : Analis memperkirakan dengan tepat bahwa pasar tetap stabil \u2192 P(B|A 2<\/sub> )=0.75
B|A 3<\/sub> : Analis memperkirakan dengan tepat bahwa pasar akan jatuh \u2192 P(B|A 3<\/sub> )=0.85<\/p>\n Untuk menentukan probabilitas seorang analis membuat prediksi bahwa pasar akan jatuh dan benar, kita perlu menggunakan rumus Teorema Bayes: <\/p>\n<\/p>\n
<\/p>\n<\/p>\n
![\"P(A_3|B)=\\cfrac{P(B|A_3)\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7c2b74ac3ed5173c4a40837675d8282d_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Kami mengganti nilai probabilitas ke dalam rumus Bayes dan menghitung probabilitasnya:<\/p>\n<\/p>\n
![\"\\begin{aligned}P(A_3|B)&=\\cfrac{P(B|A_3)\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9f98a5a8a91299aa55aab02159dcebec_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Oleh karena itu, kemungkinan seorang analis benar ketika mengatakan bahwa pasar saham akan jatuh adalah 49,42%.<\/p>\n
<\/div>\n","protected":false},"excerpt":{"rendered":"
Artikel ini menjelaskan apa itu teorema Bayes dan kegunaannya dalam probabilitas dan statistik. Dengan demikian, Anda akan menemukan apa rumus teorema Bayes, contoh penyelesaian teorema Bayes, dan apa saja penerapan teorema tersebut. Apa teorema Bayes? Dalam teori probabilitas, teorema Bayes adalah hukum yang digunakan untuk menghitung probabilitas suatu peristiwa ketika informasi apriori tentang peristiwa tersebut […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"yoast_head":"\n
\u25b7 Teorema Bayes<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan menemukan apa yang dikatakan teorema Bayes, kegunaannya, rumus teorema Bayes, dan latihan teorema Bayes yang diselesaikan.\" \/>\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\/id\/teorema-bayes\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Teorema Bayes\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan apa yang dikatakan teorema Bayes, kegunaannya, rumus teorema Bayes, dan latihan teorema Bayes yang diselesaikan.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/teorema-bayes\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-01T12:09:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/theoreme-de-bayes.png\" \/>\n<meta name=\"author\" content=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/teorema-bayes\/\",\"url\":\"https:\/\/statorials.org\/id\/teorema-bayes\/\",\"name\":\"\u25b7 Teorema Bayes\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-01T12:09:39+00:00\",\"dateModified\":\"2023-08-01T12:09:39+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan menemukan apa yang dikatakan teorema Bayes, kegunaannya, rumus teorema Bayes, dan latihan teorema Bayes yang diselesaikan.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/teorema-bayes\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/teorema-bayes\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/teorema-bayes\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Teorema bayes\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/id\/#website\",\"url\":\"https:\/\/statorials.org\/id\/\",\"name\":\"Statorials\",\"description\":\"Panduan anda untuk kompetensi statistik!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. 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![\"Rumus](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/theoreme-de-bayes.png\")
<\/figure>\n![\"P(A_i|B)\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-62ffcdb184381914ec23155ad31bbfb0_l3.png\" "\\"Rendered")
<\/p>\n![\"P(B|A_i)\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-676b61239ea67554603513360fbea72b_l3.png\" "\\"Rendered")
<\/p>\n![\"P(A_i)\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-be31252343b496b792bee3e55a99979f_l3.png\" "\\"Rendered")
<\/p>\n![\"Diagram](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/theoreme-de-probabilite-de-bayes.png\")
<\/figure>\n![\"\\begin{aligned}P(A_3|B)&=\\cfrac{P(B|A_3)\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-818d0f3336f855a1315d6a94f01d1876_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n