[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-414418-105":59,"doc-detail-414418-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-year-10-terminology-and-basic-calculations","Probability Year 10 - Terminology - and Basic Calculations","","Year 10 probability notes explain core terminology and foundational methods. It defines probability as a measure of how likely an event outcome is, using shorthand P(result), and distinguishes events, outcomes, successes, mutually exclusive results, complements, and impossible or certain outcomes. It covers numerical interpretation from 0 to 1 (and equivalent percent ranges), practical wording such as “likely,” and guidance on suitable answer forms. The notes introduce experimental vs theoretical probability, expected value, rules for combining probabilities across trials, and the use of probability trees for multi-step problems.",{"@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-year-10-terminology-and-basic-calculations/414418/",{"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-year-10-terminology-and-basic-calculations/414418.png","ImageObject",300,407,{"name":92,"@type":93},"Alex Sinclair","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-28",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does P(result) mean in these notes?","Question",{"text":112,"@type":113},"P(result) is shorthand for the probability that a particular outcome of an event happens.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you interpret mutual exclusivity using probabilities?",{"text":117,"@type":113},"Mutually exclusive outcomes are opposite cases where one or the other must happen, and their probabilities add to 1.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the expected value and how is it computed here?",{"text":121,"@type":113},"Expected value equals Probability multiplied by the number of trials. It represents the average number of successes expected, with results rounded since fractional successes aren’t possible.","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},414418,1790896167,{"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":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"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":143,"read_time":144,"preview_page_count":4},1099523882182,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Probability Year 10  \nTerminology  \nProbability measures the chance something happens. Formally, we say it measures how likely is the outcome of an event. We write P(result) as a shorthand.  \nAn event is some measurable test, measurement or observation. Sometimes trial is used instead.  \nThe results of an event are often called its outcomes. The ones we are interested in are usually termed successes, regardless of their actual type (so having blue eyes can be a “success”) .  \nMutually exclusive results are the exact opposites of each other: either one or the other must happen. Mathematically, outcomes are mutually exclusive when their probabilities add to 1.  \nThe use of“not” helps with mutually exclusive events: the opposite of“rainy” is best thought of as“not rainy” rather than vague terms such as “fine”.  \nAnother term seen sometimes is “complement”. The complement is marked with a dash, ' , and so we can write that P(A) + P(A') = 1  \nNumerical value  \nProbability is a number between 0 and 1.  \nP(X) = 0 means that the result X is impossible  \nP(X) = 1 means that the result X is certain.  \nMany students prefer to think of probability as being from 0% to 100%, which is just the same thing expressed differently.  \nStudents need be prepared to leave descriptions such as “likely” behind. They are sometimes useful to describe what a probability value means, but they are not suitable when asked for a probability. In general “likely”means a probability of greater than 0.5, becoming very likely around 0.8.  \nNo probability can be bigger than one. If students get an answer larger than 1 then they should immediately recognise that as impossible.  \nUsually answers may be given in any appropriate form: decimal, fraction or percentage.  \nPercentages are the least useful because they have to be converted before any calculations are done. In general fractions are the most useful.  \nCalculating Simple Probability  \nProbabilities can be calculated experimentally. A number of trials are conducted (or events are measured) and  \nProbability = ೙ೠ೘೙ೠ್೘೐ೝ್೐೚ೝ೑೚ೞೠ೑~~ ~~೟೎೎ೝ೔೐ೌೞ೗ೞೞ೐ೞ  \nExperimental probability is only an estimate, and will change slightly each time it is measured.  \nTheoretical probability can be calculated similarly, so long as each result (outcome) is equally likely:  \nProbability = ೞೌೠ೗೗೎೛೎೐೚ೞೞೞೞ೑೔್ೠ೗೗೐ೝೝ೐೐ೞೞೠೠ೗೗೟೟ೞೞ  \nWhen calculating theoretical probability it is important to divide up the outcomes in such a way as  \nto make them equally likely.  \n needs to be thought of as  \nso that the white is 36 of the area. The probability of white is 36.  \nThe calculation of probability is expressed as a fraction because that is, in most cases, the best way to think about the concept.  \nA probability of 0.2 means very little, but భఱ makes it much more obvious that it is one chance in five.  \nWhen calculating experimental probability we ideally test the entire population. Sometimes that isnot possible because it is too difficult, too expensive etc or the population is infinite. In those cases we take a sample and work from that. The sample needs to be:  \n– random  \n– independent (the outcome of one trial does not affect the result of the others)  \n– sufficiently large (how large depends on how accurate you need it)  \nStudents may notice that these conditions are the same as those we need for proper sampling for all statistics.  \nExpected Value  \nThe expected value is the number of successes that are expected for a certain number of trials. Expected value = Probability × number of trials  \nThe expected value is basically the same as the mean (average) number of successes, except that a mean can be a decimal value, whereas an expected value is rounded because it is not possible to have a fractional success.  \nThe probability of 6 on a normal dice is = 16. If we roll the dice 20 times we calculate 16 × 20 = 3.33 sixes on average,  \nbut the expected number of sixes is 3, since you can’t get 13 of a roll.  \nCalculations with Probabilities  \nIf ","cbCaigELVryBL7FQ","https://ap.wps.com/l/cbCaigELVryBL7FQ","pdf",120613,"English","# Terminology\n## Probability measures and notation\n## Events, outcomes, and successes\n## Mutually exclusive events and complements\n# Numerical value and interpretation\n## Probability between 0 and 1\n## Interpreting “likely” and answer formats\n# Calculating simple probability\n## Experimental vs theoretical probability\n## Sampling assumptions\n# Expected value\n## Definition and dice example\n# Calculations with probabilities\n## Addition and multiplication rules\n## Arrangements and ignoring irrelevant differences\n# Probability trees\n## Building and labeling branches","[{\"question\":\"What does P(result) mean in these notes?\",\"answer\":\"P(result) is shorthand for the probability that a particular outcome of an event happens.\"},{\"question\":\"How do you interpret mutual exclusivity using probabilities?\",\"answer\":\"Mutually exclusive outcomes are opposite cases where one or the other must happen, and their probabilities add to 1.\"},{\"question\":\"What is the expected value and how is it computed here?\",\"answer\":\"Expected value equals Probability multiplied by the number of trials. It represents the average number of successes expected, with results rounded since fractional successes aren’t possible.\"}]","Probability Year 10 - Terminology - and Basic Calculations | PDF",1790597496,15]