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It covers representations for independent and dependent events, including choosing suitable models, calculating combined-event probabilities, and using Venn diagrams, two-way tables, and tree diagrams to find expected frequencies.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/10-statistics-and-probability-103-probability-guidance-document/657363/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/10-statistics-and-probability-103-probability-guidance-document/657363.png","ImageObject",300,407,{"name":42,"@type":43},"Rhys","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What does 10.3 Probability focus on in Key Stage 4?","Question",{"text":62,"@type":63},"It breaks probability into three knowledge, skills and understanding statements, focusing on theoretical vs experimental probability and on representing and calculating probabilities for independent and dependent events.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How does relative frequency relate to theoretical probability as trials increase?",{"text":67,"@type":63},"Relative frequencies tend towards theoretical probabilities as the sample size increases, supporting understanding of long-term behaviour and the law of large numbers.",{"name":69,"@type":60,"acceptedAnswer":70},"How should teachers distinguish independent and dependent events?",{"text":71,"@type":63},"Dependent events are affected by previous outcomes, while independent events are not. Students can use this distinction to challenge misconceptions such as the gambler’s fallacy.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},657363,1793098817,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145},687207024643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","10 Statistics and probability  \nMastery Professional Development  \n10.3 Probability  \nGuidance document | Key Stage 4  \n\n| Connections |  |  |\n| --- | --- | --- |\n| Making connections |  | 2 |\n| Overview |  | 3 |\n| Prior learning |  | 4 |\n| Checking prior learning |  | 4 |\n| Key vocabulary |  | 5 |\n| Knowledge, skills and understanding |  |  |\n| Key ideas |  | 7 |\n| Exemplification |  |  |\n| Exemplified key ideas |  | 9 |\n| [10.3.1.1](10.3.1.1) | Understand that relative frequencies tend towards theoretical probabilities as sample size increases | 9 |\n| [10.3.2.2](10.3.2.2) | Understand how to choose and use a representation appropriate to the given situation | 13 |\n| [10.3.3.2](10.3.3.2) | Understand how the calculation of probabilities of combined events is affected by dependence/independence | 28 |\n| [10.3.3.4](10.3.3.4) | Find and use expected frequencies from Venn diagrams, two-way tables and tree diagrams | 34 |\n| Using these materials |  |  |\n| Collaborative planning |  | 42 |\n| Solutions |  | 42 |\n| Data sources |  | 42 |\n\nClick the heading to move to that page. Please note that these materials are principally for professional development purposes. Unlike a textbook scheme they are not designed to be directly lifted and used as teaching materials. The materials can support teachers to develop their subject and pedagogical knowledge and so help to improve mathematics teaching in combination with other high-quality resources, such as textbooks.  \n10.3 Probability  \nConnections  \nMaking connections  \nBuilding on the Key Stage 3 mastery professional development materials, the NCETM has identified a set of five 'mathematical themes' within Key Stage 4 mathematics that bring together a group of 'core concepts' .  \nThe fourth of the Key Stage 4 themes (the tenth of the themes in the suite of Secondary Mastery Materials) is Statistics and probability, which covers the following interconnected core concepts:  \n10.1 Statistical measures and analysis  \n10.2 Statistical representations and analysis  \n10.3 Probability  \nThis guidance document breaks down core concept 10.3 Probability into three statements of knowledge, skills and understanding:  \n10.3 Probability  \n10.3.1 Understand and use theoretical and experimental probability  \n10.3.2 Represent and calculate the probabilities of independent events  \n10.3.3 Represent and calculate the probabilities of dependent events  \nThen, for each of these statements of knowledge, skills and understanding we offer a set of key ideas to help guide teacher planning:  \n10.3.1 Understand and use theoretical and experimental probability  \n[10.3.1.1](10.3.1.1) Understand that relative frequencies tend towards theoretical probabilities as sample size increases  \n[10.3.1.2](10.3.1.2) Understand the meaning of mutually exclusive events and its implication for sums of probabilities  \n[10.3.1.3](10.3.1.3) Understand that knowledge of theoretical probabilities allows one to predict outcomes of future experiments  \n10.3.2 Represent and calculate the probabilities of independent events  \n[10.3.2.1](10.3.2.1) Broaden the representations used to identify all possible outcomes in a given situation  \n[10.3.2.2](10.3.2.2) Understand how to choose and use a representation appropriate to the given situation  \n[10.3.2.3](10.3.2.3) Understand how to calculate probabilities of independent events (and appreciate why)  \n10.3.3 Represent and calculate the probabilities of dependent events  \n[10.3.3.1](10.3.3.1) Understand the difference between dependent and independent events  \n[10.3.3.2](10.3.3.2) Understand how the calculation of probabilities of combined events is affected by dependence/independence  \n[10.3.3.3](10.3.3.3) Understand how to choose and use a representation appropriate to the given situation  \n[10.3.3.4](10.3.3.4) Find and use expected frequencies from Venn diagrams, two-way tablesand tree diagrams  \nOverview  \nProbability is an area of mathematics that students encounter throughout their everyday l","cbCaihbnnClgimeG","https://ap.wps.com/l/cbCaihbnnClgimeG","pdf",1809712,43,"English","# 10.3 Probability\n## Connections\n## Making connections\n## Prior learning\n## Checking prior learning\n## Key vocabulary\n## Knowledge, skills and understanding\n## Key ideas\n## Exemplification\n## Exemplified key ideas\n## 10.3.1 Understand and use theoretical and experimental probability\n## 10.3.2 Represent and calculate the probabilities of independent events\n## 10.3.3 Represent and calculate the probabilities of dependent events\n## Using these materials\n## Collaborative planning\n## Solutions\n## Data sources","[{\"question\":\"What does 10.3 Probability focus on in Key Stage 4?\",\"answer\":\"It breaks probability into three knowledge, skills and understanding statements, focusing on theoretical vs experimental probability and on representing and calculating probabilities for independent and dependent events.\"},{\"question\":\"How does relative frequency relate to theoretical probability as trials increase?\",\"answer\":\"Relative frequencies tend towards theoretical probabilities as the sample size increases, supporting understanding of long-term behaviour and the law of large numbers.\"},{\"question\":\"How should teachers distinguish independent and dependent events?\",\"answer\":\"Dependent events are affected by previous outcomes, while independent events are not. Students can use this distinction to challenge misconceptions such as the gambler’s fallacy.\"}]","10 Statistics and probability - 10.3 Probability - Guidance document | PDF",1792977998,108]