[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-572282-105":3,"detail-sidebar-cat-1-en-105":80,"doc-detail-572282-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","probability-reference-sheet-formulas-and-definitions","Probability Reference Sheet - Formulas and Definitions","","This document serves as a concise mathematical reference sheet for fundamental probability theory and combinatorial analysis. It provides essential formulas for calculating factorials, permutations, and combinations, which are foundational to counting outcomes. Additionally, it details core probability laws, including the rules for mutually exclusive events, non-mutually exclusive events, complements of events, and conditional probability. The sheet also includes guidance on converting between probability and odds, as well as calculating expected values for experiments with multiple outcomes. Designed for students and professionals, this resource offers a clear, structured overview of standard statistical operations and their application in analyzing sample spaces and event likelihood. The content is presented with specific mathematical notation and practical examples, such as the calculation of 4 factorial, to ensure clarity and ease of use in academic or quantitative environments.",{"@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/probability-reference-sheet-formulas-and-definitions/572282/",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/probability-reference-sheet-formulas-and-definitions/572282.png","ImageObject",442,249,{"name":42,"@type":43},"WPS_1790064749","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-20","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How is the number of permutations defined in this document?","Question",{"text":62,"@type":63},"The document defines permutations as P(n, k) = n! / (n - k)!, representing the number of ways to arrange k items from a set of n.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is the relationship between the probability of an event and its complement?",{"text":67,"@type":63},"The probability of the complement of an event (Ec) is calculated as P(Ec) = 1 - P(E), where P(E) is the probability of the event occurring.",{"name":69,"@type":60,"acceptedAnswer":70},"How do you calculate the expected value of an experiment?",{"text":71,"@type":63},"The expected value is calculated by summing the products of each possible outcome and its respective probability: E = P(S1) * S1 + P(S2) * S2 + ... + P(Sn) * Sn.","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},572282,1792447182,{"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":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":22,"language":135,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":12,"update_tm":139,"read_time":4},3985747859154,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Probability Reference Sheet  \nn Factorial (n!)  \nn! = n 􀀃 (n 􀀀 1) 􀀃 (n 􀀀 2) 􀀃 ::: 􀀃 3 􀀃 2 􀀃 1 Ex. 4! = 4 􀀃 3 􀀃 2 􀀃 1 = 24  \nPermutations  \nP (n; k) = (n~~!~~​k)!  \nCombinations  \nC (n; k) = k!(~~n~~n􀀀~~! ~~k)!  \nProbability of an Event Occuring  \nP (E) = ns((EE))  \nn (E) = number of elements in event Es (E) = total elements in sample space s  \nOdds in favor of an event given Probability  \nGiven probability of an event occurring equal to ~~a~~b Odds = a to b 􀀀 a  \nProbability of event occurring given odds  \nGiven odds of event E occurring equal to a to b P (E) = ab  \nProbability of Mutually Exclusive Events  \nP (AorB) = P(A) + P(B)  \nWhere A and B are mutually exclusive events  \nProbability of two events  \nP (AorB) = P(A) + P(B) 􀀀 P(AandB)  \nWhere A and B are not mutually exclusive events  \nProbability of the Compliments of an Event  \nP (Ec ) = 1 􀀀 P(E)  \nConditional Probability  \nP (BjA) = P~~ ~~(APa(nAd)B)  \nProbability that B occurs given that A occurs  \nExpectation  \nP (S1 ) 􀀃 S1 + P(S2 ) 􀀃 S2 + P(S3 ) 􀀃 S3 + ::: + P(Sn) 􀀃 Sn Where S1 ; S2 ; S3 ; :::; Sn are possible outcomes of an experiment, and P (S1 ) ; P (S2 ) ; P (S3 ) ; :::P (Sn ) are the probabilities of those events occurring","cbCaiuhgxaC8VyP6","https://ap.wps.com/l/cbCaiuhgxaC8VyP6","pdf",76616,"English","# Combinatorial Formulas\n## Factorials, Permutations, and Combinations\n# Probability Operations\n## Event Probability and Odds\n## Addition Rules for Events\n## Complements and Conditional Probability\n## Expected Value","[{\"question\":\"How is the number of permutations defined in this document?\",\"answer\":\"The document defines permutations as P(n, k) = n! / (n - k)!, representing the number of ways to arrange k items from a set of n.\"},{\"question\":\"What is the relationship between the probability of an event and its complement?\",\"answer\":\"The probability of the complement of an event (Ec) is calculated as P(Ec) = 1 - P(E), where P(E) is the probability of the event occurring.\"},{\"question\":\"How do you calculate the expected value of an experiment?\",\"answer\":\"The expected value is calculated by summing the products of each possible outcome and its respective probability: E = P(S1) * S1 + P(S2) * S2 + ... + P(Sn) * Sn.\"}]","Probability Reference Sheet - Formulas and Definitions | PDF",1791926557]