[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657360-105":59,"doc-detail-657360-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","conditional-probability-and-tree-diagrams-conditional-probability-tree-diagrams-and-card-deck-examples","Conditional Probability and Tree Diagrams - conditional probability, tree diagrams, and card-deck examples","","Conditional probability explains how event probabilities change when new information or conditions are known or imposed on an experiment. The document uses an NBA shooting example to show how estimated success rates differ under a rest condition, then introduces a standard deck card experiment to compute probabilities like P(H) and P(H|R). It emphasizes that extra information can restrict the sample space and alter the successful-event subset, which is summarized through notation such as P(H|R) and discussed in relation to tree diagrams.",{"@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/conditional-probability-and-tree-diagrams-conditional-probability-tree-diagrams-and-card-deck-examples/657360/",{"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/conditional-probability-and-tree-diagrams-conditional-probability-tree-diagrams-and-card-deck-examples/657360.png","ImageObject",300,407,{"name":92,"@type":93},"Quinn Holloway","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is conditional probability and why is it used?","Question",{"text":112,"@type":113},"Conditional probability measures the likelihood of an event when additional information about the experiment is known. It is used because the probability can change once those conditions are imposed or guaranteed.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does extra information affect the sample space in these examples?",{"text":117,"@type":113},"Additional information can restrict the sample space and change which outcomes count as successful. The document notes that conditioning effectively reduces the set of possible outcomes.",{"name":119,"@type":110,"acceptedAnswer":120},"In the card-deck example, how is P(H|R) interpreted?",{"text":121,"@type":113},"P(H|R) is the probability the card is a heart given that the card is red. The vertical bar indicates that the event R has already occurred, so probabilities are computed within the reduced sample space.","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},657360,1793096690,{"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":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":145},2336474466712,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Conditional Probability and Tree Diagrams  \nSometimes our computation of the probability of an event is changed by the knowledge that a related event has occurred (or is guaranteed to occur) or by some additional conditions imposed on the experiment. We see some examples below:  \nConditional Probability and Tree Diagrams  \nExample In a previous example, we estimated that the probability that LeBron James will make his next attempted 􀀌eld goal in a major league game is 0:567 . We used the proportion of 􀀌eld goals made out of 􀀌eld goals attempted (FG%) in the 2013/2014 season to estimate this probability. If we look at the split statistics below, we see that the FG% changes when calculated under speci􀀌ed condition. For example the FG% for games played after 3 days or more rest is 0.614 which is much higher than the overall FG% .  \nConditional Probability and Tree Diagrams  \nIf we know that LeBron's next 􀀌eld goal attempt will be made in a game after 3 days or more rest, it would be natural to use the statistic  \n Field goals made after 3+ days rest  0:614 =  \nField goals attempted after 3+ days rest to estimate the probability that he will be successful.  \nConditional Probability and Tree Diagrams  \nHere we are estimating the probability that LeBron will make the 􀀌eld goal given the extra information that the attempt will be made in a game after 3 days + rest. This is referred to as a conditional probability, because we have some prior information about conditions under which the experiment will be performed.  \nAdditional information may change the sample space and the successful event subset.  \nConditional Probability and Tree Diagrams  \nExample Let us consider the following experiment: A card is drawn at random from a standard deck of cards.  \nRecall that there are 13 hearts, 13 diamonds, 13 spades and 13 clubs in a standard deck of cards.  \nI Let H be the event that a heart is drawn,  \nI let R be the event that a red card is drawn and  \nI let F be the event that a face card is drawn, where the face cards are the kings, queens and jacks.  \nConditional Probability and Tree Diagrams  \nExample Let us consider the following experiment: A card is drawn at random from a standard deck of cards.  \nRecall that there are 13 hearts, 13 diamonds, 13 spades and 13 clubs in a standard deck of cards.  \nI Let H be the event that a heart is drawn,  \nI let R be the event that a red card is drawn and  \nI let F be the event that a face card is drawn, where the face cards are the kings, queens and jacks.  \n(a) If I draw a card at random from the deck of 52, what is P (H)?  \nConditional Probability and Tree Diagrams  \nExample Let us consider the following experiment: A card is drawn at random from a standard deck of cards.  \nRecall that there are 13 hearts, 13 diamonds, 13 spades and 13 clubs in a standard deck of cards.  \nI Let H be the event that a heart is drawn,  \nI let R be the event that a red card is drawn and  \nI let F be the event that a face card is drawn, where the face cards are the kings, queens and jacks.  \n(a) If I draw a card at random from the deck of 52, what is P (H)? 1352 = 25% .  \nConditional Probability and Tree Diagrams  \n(b) If I draw a card at random, and without showing you the card, I tell you that the card is red, then what are the chances that it is a heart?  \nConditional Probability and Tree Diagrams  \n(b) If I draw a card at random, and without showing you the card, I tell you that the card is red, then what are the chances that it is a heart? ~~ ~~1326 = 50% . If I had told you the card was black, then the sample space is all black cards, and there are 26 of those, but the successful outcomes consist of all black hearts, of which there are 0, so the probability then is ~~0~~26 .  \nConditional Probability and Tree Diagrams  \n(b) If I draw a card at random, and without showing you the card, I tell you that the card is red, then what are the chances that it is a heart? ~~ ~~1326 = 50% . If I had told you the card was bl","cbCaikPXcuwD1kRF","https://ap.wps.com/l/cbCaikPXcuwD1kRF","pdf",3283106,110,"English","# Conditional Probability and Tree Diagrams\n## Conditioning on Extra Information\n## LeBron James Rest Condition Example\n## Card Deck Experiment and Event Definitions\n## Computing P(H)\n## Computing P(H|R)","[{\"question\":\"What is conditional probability and why is it used?\",\"answer\":\"Conditional probability measures the likelihood of an event when additional information about the experiment is known. It is used because the probability can change once those conditions are imposed or guaranteed.\"},{\"question\":\"How does extra information affect the sample space in these examples?\",\"answer\":\"Additional information can restrict the sample space and change which outcomes count as successful. The document notes that conditioning effectively reduces the set of possible outcomes.\"},{\"question\":\"In the card-deck example, how is P(H|R) interpreted?\",\"answer\":\"P(H|R) is the probability the card is a heart given that the card is red. The vertical bar indicates that the event R has already occurred, so probabilities are computed within the reduced sample space.\"}]","Conditional Probability and Tree Diagrams - conditional probability, tree diagrams, and card-deck examples | PDF",1792977991,277]