[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657358-105":59,"doc-detail-657358-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-tree-diagrams-questions-1-8","Probability Tree Diagrams - Questions 1-8","","Practice set of probability tree diagram questions covering complementary events and joint probability. Includes fair spinner outcomes, counter parity selection from two bags, drawing two glasses by size, independent race wins across multiple events, sequential snooker matches with win/lose probabilities, team full-time work rates using ratio splits, conditional gym equipment usage, and repeated sampling from a bag of colored counters. Tasks focus on completing trees and calculating event probabilities such as at least one green, exactly one/ two wins, and both-red selections.",{"@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-tree-diagrams-questions-1-8/657358/",{"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-tree-diagrams-questions-1-8/657358.png","ImageObject",300,407,{"name":92,"@type":93},"Taylor Morgan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you complete a probability tree for two fair spinners?","Question",{"text":112,"@type":113},"List the possible outcomes for the first spinner, then branch the second spinner outcomes from each first outcome. Assign branch probabilities based on the spinner’s equal chances and use the resulting paths to compute the required event probability.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does “independent outcomes” mean in the race question?",{"text":117,"@type":113},"Independence means the outcome of one race does not affect the probability of winning the other race. In calculations, multiply the corresponding win probabilities for the chosen events.",{"name":119,"@type":110,"acceptedAnswer":120},"How is the probability tree affected when counters are replaced between draws?",{"text":121,"@type":113},"With replacement, each draw has the same probabilities as before. The second draw’s branch probabilities stay unchanged, so path probabilities are found by multiplying the relevant single-draw probabilities.","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},657358,1793073416,{"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":19,"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},1099523885336,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","| 1 Harry has two fair 5-sided spinners.\u003Cbr>\u003Cbr>Spinner A\u003Cbr>Harry is going to spin each spinner once.\u003Cbr>(a) Complete the probability tree diagram.\u003Cbr>Spinner A |  | \u003Cbr>Spinner B\u003Cbr>Spinner B |  |\n| --- | --- | --- | --- |\n|  |  | \u003Cbr>....................\u003Cbr>....................\u003Cbr>\u003Cbr>....................\u003Cbr>.................... | red\u003Cbr>green\u003Cbr>red\u003Cbr>green\u003Cbr>(2) |\n| \u003Cbr>....................\u003Cbr>.................... | red\u003Cbr>green |  |  |\n\n\n| (b) Work out the probability that at least one of the spinners will land on green.\u003Cbr>.......................................................\u003Cbr>(3)\u003Cbr>(Total for Question 1 is 5 marks) |\n| --- |\n|  |\n\n| 2 Cody has two bags of counters, bag A and bag B.\u003Cbr>Each of the counters has either an odd number or an even number written on it.\u003Cbr>There are 10 counters in bag A and 7 of these counters have an odd number written on them.\u003Cbr>There are 12 counters in bag B and 7 of these counters have an odd number written on them. Cody is going to take at random a counter from bag A and a counter from bag B.\u003Cbr>(a) Complete the probability tree diagram.\u003Cbr>BagA Bag B\u003Cbr>Odd\u003Cbr>number\u003Cbr>Odd number\u003Cbr>Even number\u003Cbr>Even number\u003Cbr>Odd number\u003Cbr>Even number\u003Cbr>(2)\u003Cbr>\u003Cbr>\u003Cbr>....................\u003Cbr>....................\u003Cbr>\u003Cbr>....................\u003Cbr>....................\u003Cbr>(Total for Question 2 is 2 marks) |\n| --- |\n|  |\n\n| 3 There are 20 glasses in a cupboard.\u003Cbr>13 of the glasses are large\u003Cbr>7 of the glasses are small\u003Cbr>Roberto takes at random two glasses from the cupboard.\u003Cbr>(a) Complete the probability tree diagram. |  |  |  |\n| --- | --- | --- | --- |\n| \u003Cbr>....................\u003Cbr>.................... | large | \u003Cbr>....................\u003Cbr>.................... | large\u003Cbr>small\u003Cbr>large\u003Cbr>small\u003Cbr>(2) |\n|  | small | \u003Cbr>....................\u003Cbr>.................... |  |\n| (b) Work out the probability that Roberto takes two small glasses.\u003Cbr>.......................................................\u003Cbr>(2)\u003Cbr>(Total for Question 3 is 4 marks) |  |  |  |\n|  |  |  |  |\n\n4 Emilie takes part in two races.  \nThe probability that she wins the first race is 0.7  \nThe probability that she wins the second race is 0.4  \nThe outcomes ofthe two races are independent.  \n(a) Complete the probability tree diagram.  \nFirst race Second race  \nEmilie wins  \n0.4  \nEmilie wins  \n0.7  \n.................... Emilie does  \nnot win  \nEmilie wins  \n....................  \n.................... Emilie does  \nnot win  \n.................... Emilie does  \nnot win  \n(2)  \n(b) Work out the probability that Emilie wins exactly one of the two races.  \n.......................................................  \n(3)  \n| Emilie is going to take part in a third race.\u003Cbr>If she wins both of the first two races, the probability that she will win the third race is 0.6 If she wins exactly one of the first two races, the probability that she will win the third race is 0.3 (c) Work out the probability that Emilie will win exactly two of the three races.\u003Cbr>.......................................................\u003Cbr>(3)\u003Cbr>(Total for Question 4 is 8 marks) |\n| --- |\n|  |\n\n| 5 Ding is going to play one game of snooker against each oftwo of his friends, Marco and Judd.\u003Cbr>The probability tree diagram gives information about the probabilities that Ding will win or lose each of these two games.\u003Cbr>Ding against Ding against\u003Cbr>Marco Judd\u003Cbr>0.9\u003Cbr>Ding wins\u003Cbr>Ding wins\u003Cbr>0.1 Ding loses\u003Cbr>0.25 Ding wins\u003Cbr>Ding loses\u003Cbr>0.75 Ding loses\u003Cbr>\u003Cbr>\u003Cbr>0.6\u003Cbr>0.4\u003Cbr>(a) Work out the probability that Ding will win both games.\u003Cbr>......................................................\u003Cbr>(2)\u003Cbr>(b) Work out the probability that Ding will win exactly one of the games.\u003Cbr>......................................................\u003Cbr>(3)\u003Cbr>(Total for Question 5 is 5 marks) |\n| --- |\n|  |\n\n| 6 The people working for a company work in Team A or in Team B.\u003Cbr>number of people in Team A: number of people in Team B = 3 : 4 45 of Team A work full time.\u003Cbr>24% of Team B","cbCaibto4AGqER7U","https://ap.wps.com/l/cbCaibto4AGqER7U","pdf",3388196,15,"English","# Question 1\n## Spinner A and Spinner B\n# Question 2\n## Two bags of counters\n# Question 3\n## Two glasses from a cupboard\n# Question 4\n## Two or three independent races\n# Question 5\n## Snooker against two friends\n# Question 6\n## Teams A and B full-time fractions\n# Question 7\n## Treadmill and cross trainer\n# Question 8\n## Two red/green counters with replacement","[{\"question\":\"How do you complete a probability tree for two fair spinners?\",\"answer\":\"List the possible outcomes for the first spinner, then branch the second spinner outcomes from each first outcome. Assign branch probabilities based on the spinner’s equal chances and use the resulting paths to compute the required event probability.\"},{\"question\":\"What does “independent outcomes” mean in the race question?\",\"answer\":\"Independence means the outcome of one race does not affect the probability of winning the other race. In calculations, multiply the corresponding win probabilities for the chosen events.\"},{\"question\":\"How is the probability tree affected when counters are replaced between draws?\",\"answer\":\"With replacement, each draw has the same probabilities as before. The second draw’s branch probabilities stay unchanged, so path probabilities are found by multiplying the relevant single-draw probabilities.\"}]","Probability Tree Diagrams - Questions 1-8 | PDF",1792977987,38]