[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657335-105":59,"doc-detail-657335-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","venn-diagrams-and-probability-trees-worksheet-day-68","Venn diagrams and probability trees worksheet - Day 68","","Worksheet on probability using Venn diagrams and probability trees. It includes seven questions covering set reasoning (intersection, union, complements), interpreting Venn diagrams from real-world counts, and completing probability trees for conditional events. Scenarios include sports participation, nursery children activities, eye color and freckles, drawing balls from multiple bags, sequential counter draws without replacement, bonus-dependent travel probabilities, and winning a game via a biased coin and fair die. Includes answer section with calculated results and explanations.",{"@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/venn-diagrams-and-probability-trees-worksheet-day-68/657335/",{"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/venn-diagrams-and-probability-trees-worksheet-day-68/657335.png","ImageObject",300,407,{"name":92,"@type":93},"Aria","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you calculate a probability using a Venn diagram in these questions?","Question",{"text":112,"@type":113},"Identify the relevant region in the diagram (intersection, union, or complement) and divide by the total count or total probability implied by the diagram. The worksheet asks for probabilities based on selecting a person or counting children in each section.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does completing a probability tree require?",{"text":117,"@type":113},"You must build the branches using the given conditional probabilities, then multiply along a path to get joint probabilities, or sum branches to get the overall probability. Questions Q3, Q6, and Q7 focus on tree completion and then using it to compute final probabilities.",{"name":119,"@type":110,"acceptedAnswer":120},"How is probability handled when drawing items without replacement?",{"text":121,"@type":113},"Update the sample space after the first draw, because the counts of remaining items change. 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Overall 33 children are playing tag.  \nFill in the Venn diagram to identify how many children belong in each section.  \n[3]  \nWork out 􀜲(􀜱 ∪ 􀜶)  \n  [2]  \nCopyright © 2026 Ezy Edtech Ltd. All rights reserved.  \nQ3.  \nJohn’s partner Anne is pregnant with their baby. The probability of the baby having blue eyes rather than brown eyes is 0.25 and the probability of the baby having freckles is 0.50.  \n(a) Complete the probability tree.  \n[2]  \n(b) What is the probability that John and Anne’s baby will have brown eyes and freckles?  \n  [2]  \nQ4.  \nBarry picks a ball randomly from each of three bags. Bag 1 contains three black balls and seven white balls; bag 2 contains four black balls and eight white balls; bag 3 contains ten black balls and five white balls.  \nUse the probability tree to calculate the probability of Barry picking one black ball and two white balls. Write your answer in its simplest form.  \n[4]  \nCommitted to improving learner outcomes with teacher-centric digital support.  \n2  \nQ5.  \nThere are three green counters and two red counters in a bag. Sarah picks a counter at random from the bag, and then picks a second counter without replacing the first counter. If the first counter that Sarah picks is red, what is the probability that the second counter is red?  \n  [2]  \nQ6.  \nThere is a 23 chance that Rachel will be given a bonus at the end of the year. If she gets a  \nbonus, there is a 12 chance that she will go on holiday. If she doesn’t get a bonus, there a 15 chance that she will go on holiday.  \n(a) Complete the probability tree.  \n[2]  \n(b) Work out the probability that Rachel goes on holiday.  \n  [3]  \nQ7.  \nTo win a game you have to flip a coin and then roll an unbiased die. The coin is biased and flips head 75% of the time. If you flip a head then you have to roll a 5 or a 6 to win the game. If you flip a tail you must roll a 1, 2, or 3 to win the game.  \n(a) What is the probability of winning the game?  \n  [2]  \nMartha is going to play the game 40 times. Andrew says she will lose exactly 25 games. Is Andrew correct. Use workings to support your answer.  \n[2]  \nCommitted to improving learner outcomes with teacher-centric digital support.  \n3  \nAnswers  \n1. 57/100  \n20/100 or 1/5  \n27/100  \n2.  \n3. 0.375  \n4. 41/90 5. 1/4  \n6. 12/30 →2/5 7. 3/8  \nAndrew is wrong. The expected outcome is 5/8 x 40 = 25. However, this is not exact as it is probability. You would expect the number to be around 25 but can’t predict exactly.  \nCommitted to improving learner outcomes with teacher-centric digital support.  \n4","cbCaii0fncuTldtq","https://ap.wps.com/l/cbCaii0fncuTldtq","pdf",225198,"English","# Questions\n## Venn diagram and probability tree problems\n## Answers","[{\"question\":\"How do you calculate a probability using a Venn diagram in these questions?\",\"answer\":\"Identify the relevant region in the diagram (intersection, union, or complement) and divide by the total count or total probability implied by the diagram. The worksheet asks for probabilities based on selecting a person or counting children in each section.\"},{\"question\":\"What does completing a probability tree require?\",\"answer\":\"You must build the branches using the given conditional probabilities, then multiply along a path to get joint probabilities, or sum branches to get the overall probability. Questions Q3, Q6, and Q7 focus on tree completion and then using it to compute final probabilities.\"},{\"question\":\"How is probability handled when drawing items without replacement?\",\"answer\":\"Update the sample space after the first draw, because the counts of remaining items change. In Q5, the second counter’s probability depends on whether the first counter was red or green.\"}]","Venn diagrams and probability trees worksheet - Day 68 | PDF",1792977558]