[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-657329-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-657329-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","venn-diagrams-and-conditional-probability-starter","Venn Diagrams and Conditional Probability - Starter","","Starter lesson on using Venn diagrams to interpret set relationships and conditional probability. Works through a group of 16 students taking art and music, asking for counts in overlaps and probabilities of taking art/not music, plus conditional probabilities within music-students and art-students. Includes notes on how “if” and “given” define what part of the diagram to ignore, then provides additional examples with three languages and multi-part probability questions.",{"@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/venn-diagrams-and-conditional-probability-starter/657329/",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/venn-diagrams-and-conditional-probability-starter/657329.png","ImageObject",300,407,{"name":42,"@type":43},"Lucas Martin","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How do “if” and “given” affect what you read from a Venn diagram?","Question",{"text":62,"@type":63},"They introduce a condition, telling you to ignore the parts of the Venn diagram that do not match the condition. This determines what counts form the denominator.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"In Example 1, how do you find the probability a student takes art but not music?",{"text":67,"@type":63},"Use the region representing art only (in the Venn diagram) as the numerator, and use the total number of students as the denominator.",{"name":69,"@type":60,"acceptedAnswer":70},"How do you compute conditional probability like “studies Spanish given study French”?",{"text":71,"@type":63},"Restrict the diagram to the given condition (only the French set is considered), then take the relevant overlap as the numerator and the total of that restricted set as the denominator.","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},657329,1792977548,{"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":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":95},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Venn Diagrams and Conditional Probability  \nStarter  \n1. In a group of 16 students, 12 take art and 8 take music. One student takes neither art nor music.  \n(a) Draw a Venn diagram to help you find the number of students who take both art and music.  \n(b) A student is selected at random. Find the probability the student takes art but not music.  \n(c) A music student is chosen at random. Find the probability that they do not study art.  \n(d) An art student is chosen at random. Find the probability that they also study music.  \nNotes  \nIn questions, the words“if”and “given”are often used to introduce a condition that tells us to ignore part of the Venn diagram.  \nWork on this part first as this gives us the numbers to add together to get the denominator.  \nThe numerator comes from one of the numbers that add together to get the denominator.  \nE.g. 1 The Venn diagram shows the number of students studying Spanish and French at a school.  \n(a) A student is chosen at random. Find the probability he/she studies French.  \n(b) A student is chosen at random. Find the probability he/she does not study Spanish.  \nSp Fr  \n13 2 19  \n7  \n(c) A French student is chosen at random. Find the probability he/she studies Spanish.  \n(d) A Spanish student is chosen at random. Find the probability he/she does not study French.  \nWorking: (a) “A student is chosen at random.” ≡ all students considered (41)  \nP (studies French) = ~~ ~~13~~ ~~+221919~~ ~~+~~ ~~7 = 2411 (b)  \n(c) “A French student is chosen at random.” ≡ only F is considered Total French students = 2 + 19 = 21  \nAlso study Spanish = 2  \nP (studies Spanish given study French) = 2~~ ~~19 = 221 (d)  \n[www.mathspanda.com](www.mathspanda.com)  \nE.g 2* There are 120 students in a school. 40 study Chinese (C ), 35 study Japanese (J ), and 30  \nstudy Spanish (S ) .  \n(a) Complete the Venn diagram by filling in the numbers in the missing spaces, including outside the circles.  \n(b) A student is chosen at random. Find the probability that they:  \n(i) study Chinese, Japanese and Spanish  \n(ii) Chinese and Japanese  \n(iii) Spanish and Japanese but not Chinese  \n(iv) study Japanese given that they study Chinese.  \nVideo:  Venn diagrams  \nSolutions to Starter and E.g.s  \nExercise  \nWorksheet Solving problems using Venn diagrams Qu 4-11  \n9-1 class textbook: p246 M8 .7 Qu 1-6 (Look at Qu 2 and 5 in class) A*-G class textbook: No exercise  \n9-1 homework book: p84 M8 .7 Qu 1-5  \nA*-G homework book: No exercise  \nSummary  \n“If”and “given”are often used to introduce a condition that tells us to ignore part of the Venn diagram.  \nSolving problems using Venn diagrams SOLUTIONS  \nHomework book answers (only available during a lockdown)","cbCaigwGrHOZGyhM","https://ap.wps.com/l/cbCaigwGrHOZGyhM","pdf",170581,"English","# Starter\n# Notes on “if” and “given”\n# Example 1: Art vs Music\n# Example 2: Chinese, Japanese, Spanish\n# Summary","[{\"question\":\"How do “if” and “given” affect what you read from a Venn diagram?\",\"answer\":\"They introduce a condition, telling you to ignore the parts of the Venn diagram that do not match the condition. This determines what counts form the denominator.\"},{\"question\":\"In Example 1, how do you find the probability a student takes art but not music?\",\"answer\":\"Use the region representing art only (in the Venn diagram) as the numerator, and use the total number of students as the denominator.\"},{\"question\":\"How do you compute conditional probability like “studies Spanish given study French”?\",\"answer\":\"Restrict the diagram to the given condition (only the French set is considered), then take the relevant overlap as the numerator and the total of that restricted set as the denominator.\"}]","Venn Diagrams and Conditional Probability - Starter | PDF"]