[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657332-105":59,"doc-detail-657332-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-and-probability-practice-problems","Venn Diagrams and Probability - Practice Problems","","Practice set on using Venn diagrams to construct events from a sample space and apply probability rules for unions and intersections. Includes problems on complement events (for example, having or not having blue eyes), exclusive regions (A but not B, neither A nor B), and multi-subject overlaps using student counts. Further tasks cover multiple-event shading, computing probabilities from given intersections and single-event totals, and interpreting relationships between P(A or B) and P(A) + P(B) − P(A and B).",{"@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-and-probability-practice-problems/657332/",{"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-and-probability-practice-problems/657332.png","ImageObject",300,407,{"name":92,"@type":93},"Olivia Brown","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you interpret the regions for A or B versus A and B in a Venn diagram?","Question",{"text":112,"@type":113},"A or B corresponds to the union region containing members in at least one of the events. A and B corresponds to the intersection region containing members in both events.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does “A but not B” mean when shading on a Venn diagram?",{"text":117,"@type":113},"“A but not B” is the part of event A excluding the overlap with event B, i.e., members in A only.",{"name":119,"@type":110,"acceptedAnswer":120},"How are P(A or B) and P(A) + P(B) − P(A and B) related?",{"text":121,"@type":113},"The document asks for the connection: the union probability P(A or B) equals P(A) + P(B) − P(A and B) to correct for double-counting the intersection.","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},657332,1792977553,{"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":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"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":129,"read_time":39},16904993612988,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Venn Diagrams and Probability Date:    \nA number of probability laws can be established using Venn Diagrams.  \nThis Venn diagram represents a sample space, S, of all children in a class. The event, E, shows all those students with blue eyes.  \n\n| | 15 |\n| --- | --- |\n\nS  \nDetermine the probability that a randomly selected child:  \na) has blue eyes: b) does not have blue eyes:  \nIfA and B are two events in the sample space then the event A or  \nB means that any member of this event is in `at least one of the  \nevents A or B’. This shaded region is A or B.  \nA and B means that any member of this event is in `both A and  \nB’.  \n1) Shade the region representing:  \na) in A but not in B b) neither in A nor B.  \n2) In a class of 30 students, 19 study Physics, 17 study Chemistry and 15 study both of these subjects. Display this information on a Venn diagram and determine the probability that a randomly selected class member studies:  \na) both subjects b) at least one of the subjects  \nc) Physics, but not Chemistry d) Chemistry, but not Physics  \ne) Neither subject  \nExtra Practice:  \n1) On separate Venn diagrams, using two events A and B, shade the region representing:  \na) in A b) in B  \nc) in both A and B d) in A or B  \ne) in B but not in A f) in exactly one of A or B  \n2) In a class of 40 students, 19 play tennis, 20 play netball and 8 play neither of these sports. A student is randomly chosen from the class. Determine the probability that the student:  \na) plays tennis b) does not play netball  \nc) plays at least one of the two sports d) plays one and only one of the sports  \ne) plays netball, but not tennis  \n3) 50 married women were asked whether they gave their husband flowers or chocolates for their last birthday. The results were: 31 gave chocolates, 12 gave flowers and 5 gave both chocolates and flowers. If one of the married women was chosen at random, determine the probability that she gave her husband:  \na) chocolates or flowers b) chocolates but not flowers  \nc) neither chocolates nor flowers  \n4) The medical records for a class of 30 children showed whether they had previously had measles or chickenpox. The records showed 7 had had measles, 18 had had chicken pox, and 5 had had measles and chickenpox. If one child from the class is selected randomly from the group, determine the probability that he/she has had:  \na) chicken pox b) chicken pox but not measles  \nc) neither chicken pox nor measles  \n5) Use the diagram on the right to find:  \na) P(B) b) P(A and B)  \nc) P(A or B) d) P(A) + P(B)– P(A and B)  \nWhat is the connection between c) and d)?  \n6) The 36 students in 8 classes were assigned three challenging problems, A, B and C. A poll of the classes, one week later, showed that each student had solved at least one of the problems. It also showed this additional  \ninformation.  \n• 10 students had solved all three problems  \n• 12 students had solved A and B  \n• 17 students had solved B and C  \n• 21 students had solved A and C  \n• 24 students had solved A  \n• 22 students had solved B  \n• 30 students had solved C  \na. What is the probability a student solved problem C only?  \nb. What is the probability a student solved problem A only?  \nc. What is the probability a student solved exactly one problem?  \nd. What is the probability a student solved exactly two problems?  \n7) In a class of 30 students, 17 play video games and 12 watch MTV. It turns out that 5 students play videogames and watch MTV. A student in this class is to be selected at random.  \na. What is the probability that a student plays video games?  \nb. What is the probability that a student watches MTV?  \nc. What is the probability that a student watches MTV and plays video games?  \nd. What is the probability that a student neither plays video games nor watches MTV?","cbCaic9M7alo4CmT","https://ap.wps.com/l/cbCaic9M7alo4CmT","pdf",293509,"English","# Venn diagrams and probability laws\n## Core events: blue eyes, union and intersection\n## Shading regions for A and B / complements\n## Multi-subject probability in classes\n## Extra practice with two events\n## Sports, preferences, and medical records\n## Probability identity: P(A or B) vs P(A)+P(B)-P(A and B)\n## Three-problem overlaps (A, B, C)\n## Video games and MTV overlap and complements","[{\"question\":\"How do you interpret the regions for A or B versus A and B in a Venn diagram?\",\"answer\":\"A or B corresponds to the union region containing members in at least one of the events. A and B corresponds to the intersection region containing members in both events.\"},{\"question\":\"What does “A but not B” mean when shading on a Venn diagram?\",\"answer\":\"“A but not B” is the part of event A excluding the overlap with event B, i.e., members in A only.\"},{\"question\":\"How are P(A or B) and P(A) + P(B) − P(A and B) related?\",\"answer\":\"The document asks for the connection: the union probability P(A or B) equals P(A) + P(B) − P(A and B) to correct for double-counting the intersection.\"}]","Venn Diagrams and Probability - Practice Problems | PDF"]