{"id":1939,"date":"2026-06-26T17:32:39","date_gmt":"2026-06-26T10:32:39","guid":{"rendered":"https:\/\/people.usd.ac.id\/~ydkristanto\/?page_id=1939"},"modified":"2026-06-29T18:28:06","modified_gmt":"2026-06-29T11:28:06","slug":"finding-patterns-in-repeated-random-experiments","status":"publish","type":"page","link":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/finding-patterns-in-repeated-random-experiments\/","title":{"rendered":"Finding Patterns in Repeated Random Experiments"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-right\">\n<div class=\"wp-block-button is-style-outline\"><a class=\"wp-block-button__link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/media-pengajaran\/menemukan-pola-dari-percobaan-acak-berulang\/\">ID<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-drop-cap\">Random experiments have unpredictable outcomes. But what happens if the same random experiment is repeated over and over again? Will the results continue to appear random, or will a pattern begin to emerge? In this activity, you will investigate these questions through a series of repeated random experiments.<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group alignfull has-gray-background-color has-background\"><div class=\"wp-block-group__inner-container\">\n<h3>Keeping Track of Relative Frequency<\/h3>\n\n\n\n<p>How likely do you think the spinner is to land on the red sector? Click &#8220;Spin&#8221; then click &#8220;Plot&#8221; several times to calculate and track the relative frequency.<\/p>\n\n\n\n<div class=\"wp-block-columns alignwide\">\n<div class=\"wp-block-column\">\n<figure>\n<div id=\"calculator1\" class=\"aligncenter size-full\" style=\"width: 400px; height: 400px;\"><\/div>\n<figcaption>Visualization 1: Random spinner experiment<\/figcaption>\n<\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<figure>\n<div id=\"calculator2\" class=\"aligncenter size-full\" style=\"width: 400px; height: 400px;\"><\/div>\n<figcaption>Visualization 2: Relative frequency after each spin<\/figcaption>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n<p>After repeating the experiment several times, do you notice any patterns?<\/p>\n<\/div><\/div>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Continue your investigation by adding 100 more spins at a time in <a href=\"#calculator3\">Visualization 3<\/a>. Observe how the relative frequency changes as the number of spins increases.<\/p>\n\n\n\n<figure>\n<div id=\"calculator3\" class=\"aligncenter size-full\" style=\"width: 400px; height: 400px;\"><\/div>\n<figcaption>Visualization 3: Relative frequency as the number of spins increases<\/figcaption>\n<\/figure>\n\n<script>\n  var calculator1 = Desmos.GraphingCalculator(document.getElementById('calculator1'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n  var calculator2 = Desmos.GraphingCalculator(document.getElementById('calculator2'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n  var calculator3 = Desmos.GraphingCalculator(document.getElementById('calculator3'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n\n  var state1 = {\n    \"version\": 11,\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -10,\n            \"ymin\": -25.083798882681563,\n            \"xmax\": 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\"lines\": false,\n                \"fillOpacity\": \".3\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"126\",\n                \"folderId\": \"124\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"x^{2}+y^{2}\\\\le7^{2}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"36\",\n                \"title\": \"Juring\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"38\",\n                \"folderId\": \"36\",\n                \"text\": \"Lebar sudut pusat sukses (dari sumbu-y positif searah jarum jam):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"132\",\n                \"folderId\": \"36\",\n         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\"folderId\": \"23\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(9.5-4.5,9.5\\\\right),\\\\left(5.5-4.5,9.5\\\\right),\\\\left(5.5-4.5,8\\\\right),\\\\left(9.5-4.5,8\\\\right)\\\\right)\\\\left\\\\{n_{klik}\\\\ge40\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"88\",\n                \"folderId\": \"23\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(9.5-4.5,9.5\\\\right),\\\\left(5.5-4.5,9.5\\\\right),\\\\left(5.5-4.5,8\\\\right),\\\\left(9.5-4.5,8\\\\right)\\\\right)\\\\left\\\\{n_{klik}\\\\ge40\\\\right\\\\}\",\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"u_{lang},R_{pusat}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"98\",\n                \"folderId\": \"23\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{5.5+9.5}{2}-4.5,\\\\frac{8+9.5}{2}\\\\left\\\\{n_{klik}\\\\ge40\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Reset\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"90\",\n                \"title\": \"Warna\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"91\",\n                \"folderId\": \"90\",\n                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},\n            {\n                \"type\": \"text\",\n                \"id\": \"11\",\n                \"folderId\": \"4\",\n                \"text\": \"Dasar:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"5\",\n                \"folderId\": \"4\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(0,0\\\\right),\\\\left(20,0\\\\right),\\\\left(20,1\\\\right),\\\\left(0,1\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"49\",\n                \"folderId\": \"4\",\n                \"text\": \"Kisi-kisi:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"50\",\n                \"folderId\": \"4\",\n                \"color\": 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\"color\": \"#6042a6\",\n                \"latex\": \"t_{Y}=\\\\left[0,0.25...1\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"39\",\n                \"folderId\": \"4\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=t_{ikY}\\\\left\\\\{-0.2\\\\le x\\\\le0\\\\right\\\\}\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"40\",\n                \"folderId\": \"4\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=t_{Y}\\\\left\\\\{-0.3\\\\le x\\\\le0\\\\right\\\\}\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"41\",\n                \"folderId\": \"4\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=t_{ikY}\\\\left\\\\{20\\\\le x\\\\le20.2\\\\right\\\\}\",\n      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\"type\": \"expression\",\n                \"id\": \"8\",\n                \"folderId\": \"7\",\n                \"color\": \"#000000\",\n                \"latex\": \"w_{putih}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"84\",\n                \"folderId\": \"7\",\n                \"color\": \"#c74440\",\n                \"latex\": \"w_{lightgray}=\\\\operatorname{rgb}\\\\left(211,211,211\\\\right)\"\n            }\n        ],\n        \"ticker\": {\n            \"handlerLatex\": \"j_{alan}\\\\left(\\\\operatorname{dt}\\\\right)\",\n            \"playing\": true,\n            \"open\": true\n        }\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n\n  calculator1.setState(state1);\n  calculator2.setState(state2);\n  calculator3.setState(state3);\n\n  \/\/ Source\n  var nKlik = calculator1.HelperExpression({ latex: 'n_{klik}' });\n  var sudutPusat = calculator1.HelperExpression({ latex: 'S_{pusat}' });\n  var HSukses = calculator1.HelperExpression({ latex: 'H_{sukses}' });\n\n  \/\/ Sink\n  nKlik.observe('numericValue', function() {\n    var value = nKlik.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '14', latex: `n_{klik}=${value}` });\n\t  calculator3.setExpression({ id: '52', latex: `n_{klik}=${value}` });\n    }\n  });\n  sudutPusat.observe('numericValue', function() {\n    var value = sudutPusat.numericValue;\n    if (!isNaN(value)) {\n      calculator3.setExpression({ id: '33', latex: `S_{pusat}=${value}` });\n    }\n  });\n  HSukses.observe('listValue', function() {\n    var value = HSukses.listValue;\n\tcalculator2.setExpression({ id: '22', latex: `H_{sukses}=[${value.join(',')}]` });\n\tcalculator3.setExpression({ id: '22', latex: `H_{sukses}=[${value.join(',')}]` });\n  });\n\n<\/script>\n\n\n\n<p>Based on the trend shown in <a href=\"#calculator3\">Visualization 3<\/a>, what conclusion can you draw?<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<p class=\"has-small-font-size\"><strong>What's next?<\/strong> Ready to put your new ideas to the test? Continue to <a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/uncover-the-mystery-of-the-spinner\/\">Uncover the Mystery of the Spinner<\/a> and see if you can solve the mystery!<\/p>\n<\/div><\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<div class=\"related-topics\">\n  <h3>Explore related topics<\/h3>\n  <p>Discover more contents with related topics in this website.<\/p>\n  <ul class=\"topics-list\">\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Mathematics\">Mathematics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Statistics\">Statistics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Probability\">Probability<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Relative+Frequency\">Relative Frequency<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Randomization\">Randomization<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Law+of+Large+Numbers\">Law of Large Numbers<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Data+Visualization\">Data Visualization<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Interactive+Learning+Resource\">Interactive Learning Resource<\/a><\/li>\n  <\/ul>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Random experiments have unpredictable outcomes. But what happens if the same random experiment is repeated over and over again? Will the results continue to appear random, or will a pattern begin to emerge? In this activity, you will investigate these questions through a series of repeated random experiments. Keeping Track of Relative Frequency How likely&hellip; <a class=\"more-link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/finding-patterns-in-repeated-random-experiments\/\">Continue reading <span class=\"screen-reader-text\">Finding Patterns in Repeated Random Experiments<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":1950,"parent":1140,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Finding Patterns in Repeated Random Experiments<\/title>\n<meta name=\"description\" content=\"Discover how patterns in relative frequency emerge through repeated random experiments and why it approaches the theoretical probability.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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