[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657337-105":59,"doc-detail-657337-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","venn-diagrams-probability-solutions-bronze","Venn Diagrams - Probability Solutions - Bronze","","A probability-focused Venn diagram practice set guiding learners through constructing two- and three-set region diagrams from given totals and intersections. It demonstrates how to start with the overlap, then compute outside regions using subtraction or algebraic equations. The material includes percentage-to-probability conversion, complement probability calculations, and rules for unions such as P(A or B) = P(A)+P(B)−P(A and B), applied to concrete numerical scenarios.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/venn-diagrams-probability-solutions-bronze/657337/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/venn-diagrams-probability-solutions-bronze/657337.png","ImageObject",300,407,{"name":92,"@type":93},"Noah","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why do solutions start by filling in the central overlap in a Venn diagram?","Question",{"text":112,"@type":113},"Starting with the overlap fixes the intersection value first, which then lets all surrounding regions be calculated outward using the given totals and remaining relationships.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you find the number in neither region when you know the total students and the other regions?",{"text":117,"@type":113},"Compute the outside region by subtracting the band-only, orchestra-only, and overlap values from the overall total, or form an equation and solve for the outside value.",{"name":119,"@type":110,"acceptedAnswer":120},"How is the union rule applied in probability problems with Venn diagrams?",{"text":121,"@type":113},"Use the addition formula: P(A or B) = P(A)+P(B)−P(A and B). This ensures the overlap is not double-counted when combining two sets.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657337,1793095581,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":46,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":31},8796095462418,"https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780","Venn Diagrams  \n[www. mymathscloud.com](www. mymathscloud.com) © MyMathsCloud  \nProbability: Venn Diagrams  \nTable of Contents  \n1 Bronze ........................................................................................................................ 2  \n1.1 2 events......................................................................................................................... 2  \n1.2 3 events......................................................................................................................... 9  \n2 Silver ........................................................................................................................ 12  \n2.1 3 events........................................................................................................................12  \n3 Gold ......................................................................................................................... 15  \n3.1 With Algebra ................................................................................................................15  \n4 Diamond .................................................................................................................. 18  \n4.1 With Algebra ................................................................................................................18  \nVenn Diagrams  \n[www. mymathscloud.com](www. mymathscloud.com) © MyMathsCloud  \n1 Bronze  \n1.1 2 events  \n1)  \n\n| 100 students total\u003Cbr>60 are in the band\u003Cbr>20 are in the orchestra.\u003Cbr>12 students are in both the band and the orchestra\u003Cbr>Let’s show what these 4 sentences represent these visually on a diagram\u003Cbr>\u003Cbr>Let’s put this on one diagram. We always start with filling in the central part (the overlap) . This is because after this we can easily work outwards to know the number in each region\u003Cbr>12 students are in both band and the orchestra means that the central overlap represents 12\u003Cbr>We are also given that 60 are in the band (entire left circle) and 20 are in the orchestra (entire right circle)\u003Cbr>|  |\n| --- | --- |\n| Hence\u003Cbr>Simplify | |\n\nVenn Diagrams  \n[www. mymathscloud.com](www. mymathscloud.com) © MyMathsCloud  \n2)  \nNow, the piece of information: “The Pythagoras School of Music has 100 students”, we know that the entirety of the Venn diagram should add up to 100.  \nThis means we can easily work out the outside region  \n\n| Way 1: Without Algebra\u003Cbr>Take the numbers away from the total of 100\u003Cbr>100 − 48 − 12 − 8\u003Cbr>= 32 | Way 2: Algebra (Build an equation)\u003Cbr>Assuming that the area outside of both sets is 􀀩, we can find its value using a simple equation.\u003Cbr>\u003Cbr>We know the total is 100\u003Cbr>48 + 12 + 8 + 􀀩 = 100\u003Cbr>100 = 68 + 􀀩\u003Cbr>􀀩 = 100 − 68\u003Cbr>􀀩 = 32 |\n| --- | --- |\n\nTherefore, there are 32 students that are in neither the band nor the orchestra.  \n\n| 100 total\u003Cbr>40 own a cat.\u003Cbr>25 own a dog\u003Cbr>15 own a cat and a dog\u003Cbr>Fill in the centre part (overlap) first and then we can easily work out the other regions (left and right sections)\u003Cbr>\u003Cbr>Let’s simplify the numbers and fill in the outside part\u003Cbr>|  |  |\n| --- | --- | --- |\n| i.\u003Cbr>ii.\u003Cbr>iii.\u003Cbr>iv. | !\"\\#$\"\\#$%  \"%   $\u003Cbr>= =\u003Cbr>$%% $%% !\u003Cbr>!\"\\#$%  &\"   ' $%% = $%% = !%\u003Cbr> $\"   $\"  &\u003Cbr>= =\u003Cbr>!\"\\#$\" (% )\u003Cbr> $%   $%  !\u003Cbr>= =\u003Cbr>$\"\\#$% !\" \" | |\n\nVenn Diagrams  \n[www. mymathscloud.com](www. mymathscloud.com) © MyMathsCloud  \n3)  \n\n| i.\u003Cbr>ii.\u003Cbr>iii.\u003Cbr>iv.\u003Cbr>v.\u003Cbr>vi.\u003Cbr>vii. | 20% + 30% = 50% = 0.50\u003Cbr>30% = 0.30\u003Cbr>20% + 30% + 40% = 90% = 0.90\u003Cbr>40% = 0.40\u003Cbr>100% -20% -30% -40% = 100% -90% = 10% = 0.10\u003Cbr>30% + 40% = 70% = 0.70 |  |  |  |\n| --- | --- | --- | --- | --- |\n|  | 30%\u003Cbr>20% + 30% | = | 30% 3\u003Cbr>~~ ~~ = ~~ ~~\u003Cbr>50% 5 | = 0.6 |\n\n4)  \nSmokes and gets cancer = 0.05  \nSmoke and does not get cancer = 0.20  \nDoes not smoke and gets cancer= 0.03  \nDoes not smoke and does not get cancer  \nThe sum of all probabilities = 1  \n0.05 + 0.20 + 0.03 + does not smoke and does not get cancer = 1  \nRe-arrange for does not smoke and do","cbCaitmZ5BHuKIB1","https://ap.wps.com/l/cbCaitmZ5BHuKIB1","pdf",6416550,"English","# Table of Contents\n## Bronze\n### 2 events\n### 3 events\n# Silver\n## 3 events\n# Gold\n## With Algebra\n# Diamond\n## With Algebra\n# Additional Probability Examples","[{\"question\":\"Why do solutions start by filling in the central overlap in a Venn diagram?\",\"answer\":\"Starting with the overlap fixes the intersection value first, which then lets all surrounding regions be calculated outward using the given totals and remaining relationships.\"},{\"question\":\"How do you find the number in neither region when you know the total students and the other regions?\",\"answer\":\"Compute the outside region by subtracting the band-only, orchestra-only, and overlap values from the overall total, or form an equation and solve for the outside value.\"},{\"question\":\"How is the union rule applied in probability problems with Venn diagrams?\",\"answer\":\"Use the addition formula: P(A or B) = P(A)+P(B)−P(A and B). This ensures the overlap is not double-counted when combining two sets.\"}]","Venn Diagrams - Probability Solutions - Bronze | PDF",1792977565]