[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522730-105":59,"doc-detail-522730-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-with-combinatorics-find-the-probability-of-each-event","Probability with Combinatorics - Find the probability of each event","","Probability with Combinatorics presents multiple event-based probability problems that require applying combinations and counting to compute exact likelihoods. Tasks include raffle tickets with two winners, a coin flipped ten times for exactly six heads, and a true/false guessing scenario asking for at least two correct answers. Additional problems cover selecting secret-information recipients to avoid spies, rolling a die for exactly two even results, binomial free-throw outcomes, color counts for fireworks, and card/deck or button/diamond selection with constraints.",{"@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-with-combinatorics-find-the-probability-of-each-event/522730/",{"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-with-combinatorics-find-the-probability-of-each-event/522730.png","ImageObject",300,407,{"name":92,"@type":93},"Connor ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",18,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find the probability that both Beth and Shayna win when two winners are selected from eleven raffle tickets?","Question",{"text":113,"@type":114},"Model the selection of two winners from eleven tickets and compute the probability that the two specific purchased tickets are chosen. Use combinations to compare favorable outcomes to all possible winner selections.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What probability method applies to the problem about flipping a fair coin ten times and getting exactly six heads?",{"text":118,"@type":114},"Use the binomial probability framework for independent trials. Compute the probability of exactly 6 successes (heads) out of 10 trials with probability 1/2 each.",{"name":120,"@type":111,"acceptedAnswer":121},"How is the probability of getting at most three kings in a 5-card hand from a standard deck determined?",{"text":122,"@type":114},"Treat kings as a success type in a hypergeometric setting: count the ways to choose 0, 1, 2, or 3 kings from 4 total kings and the remaining non-kings from 48. Sum those probabilities across the allowed king counts.","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},522730,1791536212,{"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":19,"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":52,"preview_page_count":4},687207022233,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Algebra 2  \nProbability with Combinatorics  \nFind the probability of each event.  \n1) Beth and Shayna each purchase one raffle ticket. If a total of eleven raffle tickets are sold and two winners will be selected, what is the probability that both Beth and Shayna win?  \n3) A fair coin is flipped ten times. What is the probability of the coin landing heads up exactly six times?  \n5) A test consists of nine true/false questions. A student who forgot to study guesses randomly on every question. What is the probability that the student answers at least two questions correctly?  \nName  Date  Period   \n2) A meeting takes place between a diplomat and fourteen government officials. However, four of the officials are actually spies. If the diplomat gives secret information to ten of the attendees at random, what is the probability that no secret information was given to the spies?  \n4) A six-sided die is rolled six times. What is the probability that the die will show an even number exactly two times?  \n6) A basketball player has a 50% chance of making each free throw. What is the probability that the player makes at least eleven out of twelve free throws?  \n7) A technician is launching fireworks near the end of a show. Of the remaining fourteen fireworks, nine are blue and five are red. If she launches six of them in a random order, what is the probability that exactly four of them are blue ones?  \n9) You are dealt five cards from a standard and shuffled deck of playing cards. Note that a standard deck has 52 cards and four of those are kings. What is the probability that you'll have at most three kings in your hand?  \n8) Ajar contains ten black buttons and six brown buttons. If nine buttons are picked at random, what is the probability that exactly five of them are black?  \n10) A bag contains six real diamonds and five fake diamonds. If six diamonds are picked from the bag at random, what is the probability that at most four of them are real?  \nKuta Software-Infinite Algebra 2  \nProbability with Combinatorics  \nFind the probability of each event.  \n1) Beth and Shayna each purchase one raffle ticket. If a total of eleven raffle tickets are sold and two winners will be selected, what is the probability that both Beth and Shayna win?  \n􀀔  \n􀀘􀀘  \n􀁼 􀀔􀀑􀀛􀀔􀀛 %  \n3) A fair coin is flipped ten times. What is the probability of the coin landing heads up exactly six times?  \n 􀀔􀀓􀀘   \n􀁼 􀀕􀀓􀀑􀀘􀀓􀀛 %􀀘􀀔􀀕  \n5) A test consists of nine true/false questions. A student who forgot to study guesses randomly on every question. What is the probability that the student answers at least two questions correctly?  \n 􀀕􀀘􀀔   \n􀁼 􀀜􀀛􀀑􀀓􀀗􀀚 %􀀕􀀘􀀙  \nName  Date  Period   \n2) A meeting takes place between a diplomat and fourteen government officials. However, four of the officials are actually spies. If the diplomat gives secret information to ten of the attendees at random, what is the probability that no secret information was given to the spies?  \n 􀀔   \n􀁼 􀀓􀀑􀀔 %􀀔􀀓􀀓􀀔  \n4) A six-sided die is rolled six times. What is the probability that the die will show an even number exactly two times?  \n 􀀔􀀘   \n􀀙􀀗  \n􀁼 􀀕􀀖􀀑􀀗􀀖􀀛 %  \n6) A basketball player has a 50% chance of making each free throw. What is the probability that the player makes at least eleven out of twelve free throws?  \n 􀀔􀀖   \n􀁼 􀀓􀀑􀀖􀀔􀀚 %􀀗􀀓􀀜􀀙  \n7) A technician is launching fireworks near the end of a show. Of the remaining fourteen fireworks, nine are blue and five are red. If she launches six of them in a random order, what is the probability that exactly four of them are blue ones?  \n 􀀙􀀓   \n􀁼 􀀗􀀔􀀑􀀜􀀘􀀛 %􀀔􀀗􀀖  \n9) You are dealt five cards from a standard and shuffled deck of playing cards. Note that a standard deck has 52 cards and four of those are kings. What is the probability that you'll have at most three kings in your hand?  \n 􀀘􀀗􀀔􀀗􀀗   \n􀁼 􀀜􀀜􀀑􀀜􀀜􀀛 %􀀘􀀗􀀔􀀗􀀘  \n8) Ajar contains ten black buttons and six brown buttons. If nine buttons are picked at random, what is the probability that exactly five of them are black","cbCaio8Uvj8oCvHz","https://ap.wps.com/l/cbCaio8Uvj8oCvHz","pdf",24436,"English","# Find the probability of each event\n## Raffle tickets and winners\n## Coin flip with exact heads count\n## True/false guessing accuracy\n## Spies and secret information\n## Die rolls with even outcomes\n## Free throws reaching a threshold\n## Fireworks color selection\n## Kings in a 5-card hand\n## Button color selection\n## Real vs fake diamonds","[{\"question\":\"How do you find the probability that both Beth and Shayna win when two winners are selected from eleven raffle tickets?\",\"answer\":\"Model the selection of two winners from eleven tickets and compute the probability that the two specific purchased tickets are chosen. Use combinations to compare favorable outcomes to all possible winner selections.\"},{\"question\":\"What probability method applies to the problem about flipping a fair coin ten times and getting exactly six heads?\",\"answer\":\"Use the binomial probability framework for independent trials. Compute the probability of exactly 6 successes (heads) out of 10 trials with probability 1/2 each.\"},{\"question\":\"How is the probability of getting at most three kings in a 5-card hand from a standard deck determined?\",\"answer\":\"Treat kings as a success type in a hypergeometric setting: count the ways to choose 0, 1, 2, or 3 kings from 4 total kings and the remaining non-kings from 48. Sum those probabilities across the allowed king counts.\"}]","Probability with Combinatorics - Find the probability of each event | PDF",1791426104]