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",{"@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-523016/523016/",{"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-523016/523016.png","ImageObject",300,407,{"name":92,"@type":93},"Đào","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",14,{"@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 the raffle?","Question",{"text":113,"@type":114},"Compute the probability each selected winner is Beth or Shayna, given 11 tickets and two winners chosen from the total. The correct result follows the conditional/random selection structure of the problem.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the probability a fair coin lands heads exactly six times in ten flips?",{"text":118,"@type":114},"Use the binomial model for independent flips, with probability of heads 1/2, and evaluate for exactly 6 successes out of 10 trials.",{"name":120,"@type":111,"acceptedAnswer":121},"How do you determine the probability of at most three kings in a hand of five cards?",{"text":122,"@type":114},"Count outcomes from a standard 52-card deck by selecting 5 cards and using combinations to include 0, 1, 2, or 3 kings among them, then divide by the total number of 5-card hands.","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},523016,1791497659,{"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},1374402968488,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Kuta Software-Infinite Geometry  \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 Geometry  \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? ","cbCaic6Ad58vuspA","https://ap.wps.com/l/cbCaic6Ad58vuspA","pdf",24384,"English","# Find the probability of each event\n## Raffle, coin, and test scenarios\n## Dice, free throws, fireworks, and selections\n## Cards, buttons, and diamonds","[{\"question\":\"How do you find the probability that both Beth and Shayna win the raffle?\",\"answer\":\"Compute the probability each selected winner is Beth or Shayna, given 11 tickets and two winners chosen from the total. The correct result follows the conditional/random selection structure of the problem.\"},{\"question\":\"What is the probability a fair coin lands heads exactly six times in ten flips?\",\"answer\":\"Use the binomial model for independent flips, with probability of heads 1/2, and evaluate for exactly 6 successes out of 10 trials.\"},{\"question\":\"How do you determine the probability of at most three kings in a hand of five cards?\",\"answer\":\"Count outcomes from a standard 52-card deck by selecting 5 cards and using combinations to include 0, 1, 2, or 3 kings among them, then divide by the total number of 5-card hands.\"}]","Probability with Combinatorics - Find the probability of each event | PDF",1791426409]