{"id":309599,"date":"2022-12-17T19:46:00","date_gmt":"2022-12-17T12:46:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=309599"},"modified":"2023-02-06T10:28:08","modified_gmt":"2023-02-06T03:28:08","slug":"ruang-sampel-dan-titik-sampel","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/ruang-sampel-dan-titik-sampel\/","title":{"rendered":"Pengertian Ruang Sampel dan Titik Sampe dengan Contohnya"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1280\" height=\"733\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/12\/pexels-steve-johnson-1006060.webp\" alt=\"\" class=\"wp-image-309601\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/12\/pexels-steve-johnson-1006060.webp 1280w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/12\/pexels-steve-johnson-1006060-768x440.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/12\/pexels-steve-johnson-1006060-1200x687.webp 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/12\/pexels-steve-johnson-1006060-1170x670.webp 1170w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, siapa di antara Quipperian yang semasa kecilnya pernah bermain tebak-tebakan uang koin? Saat uang koin dilambungkan, kamu harus menebak sisi koin yang akan muncul, misalnya muncul angka 1.000 atau gambar? Dari pelemparan itu, akan diperoleh dua kemungkinan, yaitu 50% muncul angka dan 50% muncul gambar. Baik angka maupun angklung disebut sebagai titik sampel yang merupakan anggota ruang sampel dari pelemparan uang koin. Lalu, apa yang dimaksud ruang sampel dan titik sampel? Yuk, simak selengkapnya!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Apa yang Dimaksud dengan Titik Sampel?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Sebelum membahas ruang sampel, kamu harus tahu dulu apa itu titik sampel.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Pengertian Titik Sampel<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Titik sampel adalah anggota ruang sampel yang menunjukkan kejadian itu sendiri. Banyaknya titik sampel di setiap percobaan itu berbeda-beda. Untuk menentukannya, kamu tidak perlu rumus tertentu.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Titik Sampel<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Menurut Quipperian, percobaan apa ya yang bisa dicari titik sampelnya? Cobalah untuk melemparkan sebuah koin. Kira-kira, berapa titik sampel 1 koin yang kamu lemparkan? Jawabannya sudah pasti dua, yaitu kejadian muncul angka (A) dan kejadian muncul gambar (G). Selain koin, kamu juga bisa melemparkan objek lain dengan syarat, objek tersebut memiliki beberapa sisi yang berbeda, misalnya dadu. Banyaknya titik sampel jika sebuah dadu dilempar sekali adalah 6, yaitu mata dadu 1, 2, 3, 4, 5, dan 6. Artinya, titik sampel pada pelemparan dadu mencerminkan tiap-tiap mata dadunya. Lalu, berapa titik sampel untuk 2 dadu?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Soal Titik Sampel<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Sebuah dadu dan uang koin dilempar secara bersamaan. Tentukan titik sampel yang mungkin!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pada pelemparan sebuah koin dan dadu akan menghasilkan titik sampel seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th><\/th><th>1<\/th><th>2<\/th><th>3<\/th><th>4<\/th><th>5<\/th><th>6<\/th><\/tr><\/thead><tbody><tr><td>A<\/td><td>A, 1<\/td><td>A, 2<\/td><td>A, 3<\/td><td>A, 4<\/td><td>A, 5<\/td><td>A, 6<\/td><\/tr><tr><td>G<\/td><td>G, 1<\/td><td>G, 2<\/td><td>G, 3<\/td><td>G, 4<\/td><td>G, 5<\/td><td>G, 6<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Soal selanjutnya <em>nih<\/em> Quipperian, tapi dibuat PR, ya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Berapa banyak titik sampel yang mungkin terjadi pada percobaan melempar 5 koin uang?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Apa yang Dimaksud dengan Ruang Sampel?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan ruang sampel erat kaitannya dengan teori peluang atau probabilitas. Untuk mendapatkan ruang sampel, seseorang harus melakukan percobaan terlebih dahulu. Lalu, apa pengertian ruang sampel?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Pengertian Ruang Sampel<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Ruang sampel adalah seluruh kemungkinan yang muncul dari suatu kejadian atau percobaan. Artinya, di dalam ruang sampel memuat semua titik sampel yang mungkin dari suatu kejadian. Misalnya saat kamu melemparkan sebuah dadu, semua kemungkinan yang muncul adalah 1, 2, 3, 4, 5, dan 6. Nah, himpunan dari {1, 2, 3, 4, 5, 6} itulah yang disebut sebagai ruang sampel. Secara matematis, lambang ruang sampel adalah S dan banyaknya elemen di dalamnya memiliki lambang n(S).&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Ruang Sampel<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Tanpa ada kejadian atau percobaan, kamu tidak bisa menentukan ruang sampel ya. Salah satu percobaan yang bisa kamu ambil adalah pada pelemparan sebuah koin seperti contoh sebelumnya. Ruang sampel dari sebuah koin adalah S = {A, G} di mana A = kejadian muncul angka dan G = kejadian muncul gambar. Oleh karena banyaknya elemen di dalam ruang sampel ada dua, maka n(S) = 2. Lalu, berapa ruang sampel untuk 3 koin? Temukan di pembahasan selanjutnya, ya.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Cara Mencari Ruang Sampel<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Susunan ruang sampel akan berpengaruh pada nilai akhir peluang yang dihasilkan. Oleh sebab itu, kamu harus tahu bagaimana cara membuat ruang sampel yang benar. Ruang sampel bisa dibuat dengan tiga cara, yaitu dengan pasangan berurutan, tabel, dan diagram pohon. Lalu, bagaimana bentuk ketiganya?<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Cara Pasangan Berurutan<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Cara ini akan efektif untuk kamu gunakan pada percobaan yang memiliki sedikit titik sampel. Misalnya pelemparan 1 atau 2 koin dan pelemparan satu buah dadu. Cara menyusun anggota ruang sampel dengan pasangan berurutan adalah sebagai berikut.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Tentukan dahulu titik sampel percobaannya.<\/li>\n\n\n\n<li>Buat ruang sampelnya dalam bentuk himpunan<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Perhatikan contoh berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Saat kamu melemparkan 1 buah dadu, kemungkinan titik sampel yang muncul adalah 1, 2, 3, 4, 5, 6. Dengan demikian, ruang sampelnya adalah S = {1, 2, 3, 4, 5, 6} dengan banyaknya elemen (n(S)) = 6.<\/li>\n\n\n\n<li>Saat kamu melemparkan dua buah koin, kemungkinan titik sampel muncul adalah (AA), (AG), (GA), dan (GG). Dengan demikian ruang sampelnya adalah S = {(AA), (AG), (GA), dan (GG)} dengan n(S) = 4.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Cara Tabel<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk kejadian yang memiliki titik sampel cukup banyak, cara pasangan berurutan dinilai kurang efektif. Oleh sebab itu, kamu bisa menggunakan tabel. Misalnya 2 buah dadu dilempar bersama-sama, banyaknya anggota ruang sampelnya adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th><\/th><th>1<\/th><th>2<\/th><th>3<\/th><th>4<\/th><th>5<\/th><th>6<\/th><\/tr><\/thead><tbody><tr><td><strong>1<\/strong><\/td><td>(1, 1)<\/td><td>(1, 2)<\/td><td>(1, 3)<\/td><td>(1, 4)<\/td><td>(1, 5)<\/td><td>(1, 6)<\/td><\/tr><tr><td><strong>2<\/strong><\/td><td>(2, 1)<\/td><td>(2, 2)<\/td><td>(2, 3)<\/td><td>(2, 4)<\/td><td>(2, 5)<\/td><td>(2, 6)<\/td><\/tr><tr><td><strong>3<\/strong><\/td><td>(3, 1)<\/td><td>(3, 2)<\/td><td>(3, 3)<\/td><td>(3, 4)<\/td><td>(3, 5)<\/td><td>(3, 6)<\/td><\/tr><tr><td><strong>4<\/strong><\/td><td>(4, 1)<\/td><td>(4, 2)<\/td><td>(4, 3)<\/td><td>(4, 4)<\/td><td>(4, 5)<\/td><td>(4, 6)<\/td><\/tr><tr><td><strong>5<\/strong><\/td><td>(5, 1)<\/td><td>(5, 2)<\/td><td>(5, 3)<\/td><td>(5, 4)<\/td><td>(5, 5)<\/td><td>(5, 6)<\/td><\/tr><tr><td><strong>6<\/strong><\/td><td>(6, 1)<\/td><td>(6, 2)<\/td><td>(6, 3)<\/td><td>(6, 4)<\/td><td>(6, 5)<\/td><td>(6, 6)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari tabel di atas, berapa titik sampel dari 2 dadu? Jawabannya adalah 36.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, ruang sampelnya adalah himpunan dari semua titik sampel yang tertera pada tabel, sehingga n(S) = 36.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cara tabel juga bisa kamu gunakan untuk menentukan ruang sampel pada pelemparan 3 koin. Berapa ruang sampel pada 3 koin? Yuk, cekidot!<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th><\/th><th>AA<\/th><th>AG<\/th><th>GA<\/th><th>GG<\/th><\/tr><\/thead><tbody><tr><td><strong>A<\/strong><\/td><td>AAA<\/td><td>AAG<\/td><td>AGA<\/td><td>AGG<\/td><\/tr><tr><td><strong>G<\/strong><\/td><td>GAA<\/td><td>GAG<\/td><td>GGA<\/td><td>GGG<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Cara Diagram Pohon<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Diagram pohon adalah cara menentukan ruang sampel menggunakan garis hubung. Ambil contoh pelemparan tiga koin seperti pada cara tabel.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/DmW6XoFPkqX6qvCTqWw_x4xaqpKMfrQUkoI3GZOvWvRPjXuDjFn_BQxUM6zVaWAV_PuWJJ_j-S4pAjAwOcg4RnFHlWV1D5020MD4aPNjVTCIwAA2341UYM1_wEg5dl_hh1k2EyHunDEolj7TLDT9JxVtHJf980uHtdQ9Sfey2Rf21R1edeLe8wLa1dwuqBEbUjr47x8obQ\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari uraian diagram pohon di atas, ternyata diperoleh titik sampel yang sama kan dengan cara tabel? Berdasarkan hasil tersebut, ruang sampel pada pelemparan tiga koin adalah S = {(AAA), (AAG), (AGA), (AGG), (GAA), (GAG), (GGA), (GGG)} dengan n(S) = 8.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Semakin banyak jumlah koin yang dilemparkan bersama-sama, semakin banyak cabang pada diagramnya. Kalau begitu, berapa ruang sampel dari 4 koin?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Soal Ruang Sampel<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Dalam rangka pemilihan ketua OSIS beserta wakilnya, SMA Harapan Bangsa menggelar rapat terbuka untuk memilih formasi yang sesuai dengan 8 kandidat terpilih. Dari hasil seleksi, empat kandidat dinyatakan layak menjadi calon ketua OSIS dan empat sisanya ditempatkan sebagai calon wakil ketua OSIS. Adapun calon ketua OSISnya adalah Rendi, Heru, Brian, dan Ambar. Sementara calon wakil ketua OSISnya adalah Ferdian, Vani, Lusi, dan Dimas. Tentukan pasangan formasi yang mungkin untuk para kandidat beserta jumlahnya!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Formasi yang mungkin untuk para kandidat menunjukkan ruang sampel. Kamu bisa menggunakan cara tabel atau diagram pohon. Pada kesempatan ini, Quipper Blog akan memilih cara tabel, ya.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th><\/th><th>Ferdian<\/th><th>Vani<\/th><th>Lusi<\/th><th>Dimas<\/th><\/tr><\/thead><tbody><tr><td>Rendi<\/td><td>Rendi, Ferdian<\/td><td>Rendi, Vani<\/td><td>Rendi, Lusi<\/td><td>Rendi, Dimas<\/td><\/tr><tr><td>Heru<\/td><td>Heru, Ferdian<\/td><td>Heru, Vani<\/td><td>Heru, Lusi<\/td><td>Heru, Dimas<\/td><\/tr><tr><td>Brian&nbsp;<\/td><td>Brian, Ferdian<\/td><td>Brian, Vani<\/td><td>Brian, Lusi<\/td><td>Brian, Dimas<\/td><\/tr><tr><td>Ambar<\/td><td>Ambar, Ferdian<\/td><td>Ambar, Vani<\/td><td>Ambar, Lusi<\/td><td>Ambar, Dimas<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, pasangan formasi yang mungkin adalah S = {(Rendi, Ferdian), (Rendi, Vani), (Rendi, Lusi), (Rendi, Dimas), (Heru, Ferdian), (Heru, Vani), (Heru, Lusi), (Heru, Dimas), (Brian, Ferdian), (Brian, Vani), (Brian, Lusi), (Brian, Dimas), (Ambar, Ferdian), (Ambar, Vani), (Ambar, Lusi), (Ambar, Dimas)} dan n(S) = 16.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Apa Perbedaan Ruang Sampel dan Titik Sampel?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Dari pembahasan di atas, sudah jelas kan apa perbedaan ruang sampel dan titik sampel. Ruang sampel menunjukkan semua kemungkinan yang muncul pada suatu kejadian. Nah, setiap anggota ruang sampel itulah yang disebut titik sampel.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Agar belajarmu tambah semangat, coba tentukan ruang sampel kartu bridge!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog kali ini. Semoga bermanfaat ya. Untuk mendapatkan materi lengkapnya, yuk buruan gabung Quipper Video. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, siapa di antara Quipperian yang semasa kecilnya pernah bermain tebak-tebakan uang koin? Saat uang koin dilambungkan, kamu harus menebak sisi koin yang&hellip;<\/p>\n","protected":false},"author":156447303,"featured_media":309601,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384865],"tags":[679386714],"ppma_author":[679386823,679386836],"class_list":["post-309599","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-matematika-kelas-8"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pengertian Ruang Sampel dan Titik Sampe dengan Contohnya - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Apa itu ruang sampel dan titik sampel? 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