[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-414406-105":59,"doc-detail-414406-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","probability-terminology-and-examples-1805-spring-2018","Probability - Terminology and Examples - 18.05 Spring 2018","","Probability terminology and examples explain key concepts used in introductory probability: experiments, sample spaces, events as subsets, and the probability function P(x) that assigns probabilities to outcomes. The material includes core probability constraints (each probability between 0 and 1, total probability summing to 1) and worked coin-toss examples. It also covers discrete versus infinite sample spaces, event descriptions in words and notation, Venn-diagram interpretations, and logic questions about disjointness and implication between events.",{"@graph":69,"@context":123},[70,84,106],{"@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-terminology-and-examples-1805-spring-2018/414406/",{"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-terminology-and-examples-1805-spring-2018/414406.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-08","2026-09-28",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are the basic parts of a probability problem described in the slides?","Question",{"text":113,"@type":114},"An experiment produces outcomes from a sample space, and an event is a subset of the sample space. The probability function P assigns a probability to each outcome.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What rules must hold for probabilities in the sample space?",{"text":118,"@type":114},"Each probability lies between 0 and 1. The total probability across all possible outcomes is 1.",{"name":120,"@type":111,"acceptedAnswer":121},"How are events related when they are disjoint or when one implies another?",{"text":122,"@type":114},"Two events can be disjoint, meaning they cannot happen at the same time (the slides state “exactly 2 heads” and “exactly 2 tails” are disjoint). The slides also note that “at least 2 heads” implies “exactly two heads.”","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},414406,1790799825,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":46,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":31,"preview_page_count":4},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068","Probability: Terminology and Examples  \n18.05 Spring 2018  \nProbability Cast  \nIntroduced so far  \n Experiment: a repeatable procedure  \n Sample space: set of all possible outcomes S (or 􀀊) .  \n Event: a subset of the sample space.  \n Probability function, P (!): gives the probability for each outcome ! 2 S  \n1. Probability is between 0 and 1  \n2. Total probability of all possible outcomes is 1 .  \nFebruary 12, 2018 2 / 19  \nExample (from the reading)  \nExperiment: toss a fair coin, report heads or tails.  \nSample space: 􀀊 = fH ; Tg.  \nProbability function: P (H) = :5, P (T ) = :5.  \nUse tables:  \nOutcomes  H T  \nProbability  1/2 1/2  \n(Tables can really help in complicated examples)  \nFebruary 12, 2018 3 / 19  \nDiscrete sample space  \nDiscrete = listable  \nExamples:  \nfa, b, c, dg (􀀌nite)  \nf0, 1, 2,   g (in􀀌nite)  \nfsun,cloud,rain,snow,fogg  \nfpatient cured, unchanged, patient diedg  \nFebruary 12, 2018 4 / 19  \nEvents  \nEvents are sets:  \n Can describe in words  Can describe in notation  \n Can describe with Venn diagrams Experiment: toss a coin 3 times.  \nEvent:  \nYou get 2 or more heads = f HHH, HHT, HTH, THHg  \nFebruary 12, 2018 5 / 19  \nEvents, sets and words  \nExperiment: toss a coin 3 times.  \nWhich of following equals the event \\exactly two heads\"?  \nA = fTHH ; HTH ; HHT ; HHHg B = fTHH ; HTH ; HHTg C = fHTH ; THHg  \n(1) A (2) B (3) C (4) A or B  \nFebruary 12, 2018 6 / 19  \nEvents, sets and words  \nExperiment: toss a coin 3 times.  \nWhich of the following describes the event fTHH ; HTH ; HHTg?  \n(1) \\exactly one head\"  \n(2) \\exactly one tail\"  \n(3) \\at most one tail\"  \n(4) none of the above  \nFebruary 12, 2018 7 / 19  \nEvents, sets and words  \nExperiment: toss a coin 3 times.  \nThe events \\exactly 2 heads\" and \\exactly 2 tails\" are disjoint.  \n(1) True (2) False  \nFebruary 12, 2018 8 / 19  \nEvents, sets and words  \nExperiment: toss a coin 3 times.  \nThe event \\at least 2 heads\" implies the event \\exactly two heads\".  \n(1) True (2) False  \nFebruary 12, 2018 9 / 19  \nProbability rules in mathematical notation  \nSample space: S = f!1 ; !2 ; : : : ; ! ng  \nOutcome: ! 2 S  \nProbability between 0 and 1:  \nTotal probability is 1: Event A: P (A)  \nFebruary 12, 2018 10 / 19","cbCaitVtl0pbhcd2","https://ap.wps.com/l/cbCaitVtl0pbhcd2","pdf",262626,"English","# Probability terminology and examples\n## Experiments, sample spaces, and events\n## Probability function and probability rules\n## Discrete sample spaces\n## Event descriptions and example questions","[{\"question\":\"What are the basic parts of a probability problem described in the slides?\",\"answer\":\"An experiment produces outcomes from a sample space, and an event is a subset of the sample space. The probability function P assigns a probability to each outcome.\"},{\"question\":\"What rules must hold for probabilities in the sample space?\",\"answer\":\"Each probability lies between 0 and 1. The total probability across all possible outcomes is 1.\"},{\"question\":\"How are events related when they are disjoint or when one implies another?\",\"answer\":\"Two events can be disjoint, meaning they cannot happen at the same time (the slides state “exactly 2 heads” and “exactly 2 tails” are disjoint). The slides also note that “at least 2 heads” implies “exactly two heads.”\"}]","Probability - Terminology and Examples - 18.05 Spring 2018 | PDF",1790597476]