[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657345-105":59,"doc-detail-657345-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","probability-sample-spaces-and-tree-diagrams","Probability - Sample Spaces and Tree Diagrams","","This educational material provides a structured exercise set for students learning to represent probability problems using various visual models. The document centers on a scenario involving a bag containing 3 red balls and 5 blue balls, where a ball is selected with replacement and a second selection follows. The exercises guide the user through constructing sample space diagrams, frequency trees, and probability tree diagrams to calculate the likelihood of specific events. Key learning objectives include understanding independent events, simplifying complex outcome representations, and calculating the probability of combined outcomes such as picking two red balls, two blue balls, or one ball of each color. By systematically working through these methods, students develop a conceptual understanding of how replacement affects individual trial outcomes and how tree diagrams facilitate the clear identification of total and successful outcomes in a probability experiment.",{"@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/probability-sample-spaces-and-tree-diagrams/657345/",{"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/probability-sample-spaces-and-tree-diagrams/657345.png","ImageObject",300,407,{"name":92,"@type":93},"Miles","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the probability of picking two red balls with replacement?","Question",{"text":112,"@type":113},"Since there are 3 red balls and 5 blue balls (8 total), the probability of picking a red ball is 3/8. For two red balls with replacement, the probability is 3/8 * 3/8 = 9/64.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does replacement affect the probability calculation?",{"text":117,"@type":113},"With replacement, the total number of balls and the count of each color remain constant for the second draw, ensuring that the two picks are independent events.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the purpose of a probability tree diagram in this context?",{"text":121,"@type":113},"A probability tree diagram helps visualize all possible outcomes of the two-step experiment and simplifies the calculation of combined event probabilities by multiplying along the branches.","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},657345,1792977591,{"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":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"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":52},13056703019404,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Probability, Sample Spaces and Tree Diagrams  \nA. Draw a sample space diagram for this problem. How many different outcomes are there?  \n\n|  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n\nB. Can we describe this information in a simpler way?  \n\n|  |  |  |\n| --- | --- | --- |\n|  |  |  |\n|  |  |  |\n\nC. Here is a different way to show this information – a frequency tree.  \nD. We can also draw a probability tree diagram. This helps think about the total number of outcomes.  \nE. For each diagram, what is the probability of picking:  \na) Two red balls  \nb) Two blue balls  \nc) One ball of each colour  \nd) Both balls the same colour  \nProbability, Sample Spaces and Tree Diagrams  \nA. Draw a sample space diagram for this problem. How many different outcomes are there?  \n\n|  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n\nB. Find a way to simplify the drawing  \n\n|  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n\nC. Show this information in a frequency tree  \nD. Now show probabilities on a tree diagram  \nE. What is the probability of picking:  \ne) Two red balls  \nf) Two blue balls  \ng) One ball of each colour  \nh) Both balls the same colour","cbCaidrzU7JQ7mHK","https://ap.wps.com/l/cbCaidrzU7JQ7mHK","pdf",186565,"English","# Probability Exercises\n## Drawing Sample Space Diagrams\n## Simplifying Data Representation\n## Frequency Tree Analysis\n## Probability Tree Diagrams\n## Probability Calculation Tasks","[{\"question\":\"What is the probability of picking two red balls with replacement?\",\"answer\":\"Since there are 3 red balls and 5 blue balls (8 total), the probability of picking a red ball is 3/8. For two red balls with replacement, the probability is 3/8 * 3/8 = 9/64.\"},{\"question\":\"How does replacement affect the probability calculation?\",\"answer\":\"With replacement, the total number of balls and the count of each color remain constant for the second draw, ensuring that the two picks are independent events.\"},{\"question\":\"What is the purpose of a probability tree diagram in this context?\",\"answer\":\"A probability tree diagram helps visualize all possible outcomes of the two-step experiment and simplifies the calculation of combined event probabilities by multiplying along the branches.\"}]","Probability - Sample Spaces and Tree Diagrams | PDF"]