[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-189816-105":3,"detail-sidebar-cat-1-en-105":80,"doc-detail-189816-en":126},{"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","summary-of-set-operations-and-probability-equivalents","Summary of set operations and probability equivalents","","This document provides a summary of set operations and their equivalents in probability theory, presented in Table 1. It details the notation for various set operations, such as intersection, union, and complement, and maps them to corresponding probability terminology like sample space, event, and certain event. Additionally, Table 2 presents an example of cell lifetime analysis, categorizing cells by their lifetime (less than 1000 hours, 1000-1500 hours, and greater than 1500 hours) and providing the number and proportion of cells in each category. The analysis indicates that 22.5% of cells have a lifetime under 1000 hours, 40% live between 1000 and 1500 hours, and 37.5% live longer than 1500 hours. The document appears to be educational or analytical in nature, likely serving as a reference or instructional material for topics in set theory and statistics.",{"@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/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/general/","General",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/summary-of-set-operations-and-probability-equivalents/189816/",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/summary-of-set-operations-and-probability-equivalents/189816.png","ImageObject",442,249,{"name":42,"@type":43},"Angel","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-09-20","2026-09-03",true,{"@type":52,"interactionType":53,"userInteractionCount":26},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What are the probability equivalents of set operations shown in Table 1?","Question",{"text":62,"@type":63},"Table 1 shows that the set operation 'S' (sample space) corresponds to 'all outcomes' in probability, 'A ∩ B' (intersection) corresponds to 'both A and B', and 'A U B' (union) corresponds to 'either A or B, or both'.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is the total proportion of cells in the lifetime analysis?",{"text":67,"@type":63},"The total proportion of cells in the lifetime analysis is the sum of the proportions for each category: 0.225 + 0.400 + 0.375 = 1.000, representing 100% of the cells analyzed.",{"name":69,"@type":60,"acceptedAnswer":70},"What is the most common lifetime range for cells in the example?",{"text":71,"@type":63},"The most common lifetime range for cells in the example is 1000–1500 hours, with 80 cells representing 40.0% of the total.","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},189816,1788399425,{"code":4,"msg":81,"data":82},"success",[83,88,93,98,103,108,113,118,123],{"id":84,"doc_module":22,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},11,"Presentations",90,"presentations",{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},12,"Resumes",80,"resumes",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},14,"Invoices",70,"invoices",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},15,"Posters",60,"posters",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},16,"Social Media",50,"social-media",{"id":109,"doc_module":22,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},17,"Forms",40,"forms",{"id":114,"doc_module":22,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},18,"Letters",30,"letters",{"id":119,"doc_module":22,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},21,"Paper Templates",5,"papers-templates",{"id":124,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":4,"slug":125},158,"general-158",{"code":4,"msg":81,"data":127},{"doc_id":78,"user_id":128,"nickname":42,"user_avatar":129,"doc_module":22,"category_id":124,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":26,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":135,"language":136,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":12,"update_tm":79,"read_time":33},687207412472,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","| Table 1. Summary of set operations and probability equivalents\u003Cbr>Таблица 1. Эквиваленты операций над множествами в теории вероятностей |  |  |\n| --- | --- | --- |\n| Notation | Set terminology | Probability terminology |\n| S\u003Cbr>s\u003Cbr>A Ā, Ac\u003Cbr>A ∩ B\u003Cbr>A ⋃ BA \\ B\u003Cbr>A ∆ B\u003Cbr>A ∈ B\u003Cbr>Ø S | All outcomes Point in S Subset of S Complement of A Intersection Union\u003Cbr>Difference\u003Cbr>Symmetric difference Inclusion Empty set Whole space | Sample space Elementary event, outcome Event where some outcome inA occurs Event where no outcome inA occurs Both A and B Either A or B, or both A, but not B Either A or B, but not both IfA, then B Impossible event Certain event |\n\n| Table 2. Lifetime of cells analysis example\u003Cbr>Таблица 2. Пример анализа продолжительности жизни\u003Cbr>клеток |  |  |\n| --- | --- | --- |\n| Lifetime, h | Number of cells | Proportion |\n| \u003C1000 | 45 | 0.225 |\n| 1000–1500 | 80 | 0.400 |\n| >1500 | 75 | 0.375 |","cbCaisx52elvRJPG","https://ap.wps.com/l/cbCaisx52elvRJPG","pdf",1345635,10,"English","# Table 1. Summary of set operations and probability equivalents\n## Notation\n## Set terminology\n## Probability terminology\n# Table 2. Lifetime of cells analysis example","[{\"question\":\"What are the probability equivalents of set operations shown in Table 1?\",\"answer\":\"Table 1 shows that the set operation 'S' (sample space) corresponds to 'all outcomes' in probability, 'A ∩ B' (intersection) corresponds to 'both A and B', and 'A U B' (union) corresponds to 'either A or B, or both'.\"},{\"question\":\"What is the total proportion of cells in the lifetime analysis?\",\"answer\":\"The total proportion of cells in the lifetime analysis is the sum of the proportions for each category: 0.225 + 0.400 + 0.375 = 1.000, representing 100% of the cells analyzed.\"},{\"question\":\"What is the most common lifetime range for cells in the example?\",\"answer\":\"The most common lifetime range for cells in the example is 1000–1500 hours, with 80 cells representing 40.0% of the total.\"}]","Summary of set operations and probability equivalents | PDF"]