[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657366-105":59,"doc-detail-657366-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","lesson-10-8-tree-diagrams","Lesson 10-8 - Tree Diagrams","","Lesson 10-8 focuses on using tree diagrams and probability rules to calculate probabilities for combined events. It explains how to place individual branch probabilities, multiply probabilities along a path to get an outcome, and use addition when multiple branches contribute. Practice covers independent and dependent scenarios, including repeated coin outcomes, sequential traffic lights, drawing sweets without replacement, and selecting biscuits or calculators where probabilities depend on the previous choice. It concludes with problems requiring conditional probability and independence decisions.",{"@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/lesson-10-8-tree-diagrams/657366/",{"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/lesson-10-8-tree-diagrams/657366.png","ImageObject",300,407,{"name":92,"@type":93},"Connor ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you calculate the probability of a specific outcome on a tree diagram?","Question",{"text":112,"@type":113},"Multiply the probabilities along the branches that make up that outcome path.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"When do you add probabilities in a tree diagram question?",{"text":117,"@type":113},"Add probabilities when the question asks for an event that occurs through more than one branch (multiple possible paths).",{"name":119,"@type":110,"acceptedAnswer":120},"What is the difference between independent and dependent events in these lessons?",{"text":121,"@type":113},"Independent events mean one event does not affect the other, while dependent events mean the outcome of one affects the probability of the other.","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},657366,1793065536,{"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":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":46},687207022233,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Name  Date:    \nLesson 10-8: Tree Diagrams  \nLearning Goals:  \n\\#9: How do we use tree diagrams and probability rules to determine the probability of combined events?  \nUsing Tree Diagrams  \nExample: What is the probability of a flipping a fair coin 2 times, and each landing on heads? Let's look at this on a tree diagram...  \nWorking with Tree Diagrams  \nSTEP 1: Write each individual probability on the appropriate branch.  \nSTEP 2: To find the probability of a given outcome, multiply the probabilities along the branches. STEP 3: If asked to find the probability of more than one “branch”, add your probabilities together.  \nExample: Consider two archers firing simultaneously at a target. Li has a 3/4 chance of hitting a target and Yuka has a 4/5 chance of hitting a target. The tree diagram for this information is given below.  \nIB QUESTIONS  \n􀁸  RECALL: Two events are independent events when the occurrence of one event does not affect the occurrence of the other.  \n􀁸  RECALL: Two events are dependent events when the occurrence of one event does affect the occurrence of the other.  \nWe Try! 􀃆 Practice with Independent Events  \n1) A teacher has a box containing six type A calculators and four type B calculators.  \nThe probability that a type A calculator is faulty is 0.1 and the probability that a type B calculator is faulty is 0.12.  \n(a) Complete the tree diagram given below, showing all the probabilities.  \ntypeA  \ntypeB  \nFAULTY  \nNOTFAULTY  \nFAULTY  \nNOTFAULTY  \n(b) A calculator is selected at random from the box. Find the probability that the calculator is  \n(i) a faulty type A;  \n(ii) not faulty;  \nYou Try! 􀃆 Practice with Independent Events  \n2) Jim drives to work each day through two sets of traffic lights. The probability of the first set of traffic lights being red is 0.65. If the first set is red then the probability that the next set of traffic lights is red is 0.46. If the first set is not red, the probability that the next set is red is 0.72.  \nred  \nnot  \nred  \nred  \nnot  \nred  \nred  \nnot  \nred  \na) Complete the tree diagram above.  \nb) Calculate the probability that  \ni. the second set of traffic lights is red  \nii. both traffic lights are red  \niii. a traffic light is not red  \nWe Try! 􀃆 Practice with Dependent Events  \n3) A bag contains two red sweets and three green sweets. Jacques takes one sweet from the bag, notes its colour, then eats it. He then takes another sweet from the bag.  \na) Complete the tree diagram below to show all probabilities.  \nRed  \nGreen  \nRed  \nGreen Red  \nGreen  \nb) Find the probability of  \n\n| i. drawing a red sweet. | ii. not drawing a red sweet. |\n| --- | --- |\n| iii. drawing red and then a green sweet. | iv. drawing a red and a green sweet. |\n| v. both sweets being green | vi. both sweets being the same colour. |\n\nYou Try! 􀃆 Practice with Dependent Events  \n4) There is a biscuit tin on a shelf. The tin contains one chocolate biscuit and nine plain biscuits.  \nA child chooses a biscuit from the tin. The child eats the biscuit and chooses another one from the tin. The tree diagram below represents the possible outcomes for this event.  \nC  \nP  \nC  \nP C  \nP  \n(i) Write down the values ofa and b.  \n(ii) Complete the tree diagram above to show all probabilities.  \n(iii) Find the probability that both biscuits are chocolate.  \n(iv) What is the probability that at least one of the biscuits is chocolate?  \nName  Date:    \nLesson 10-8 Homework  \n1) Sandra is attempting an exam question. She has to choose two correct statements from a list of five. Below is a tree diagram showing Sandra’s possible choices. One of the probability values is missing.  \ncorrect  \n–3 incorrect 4  \n—  \n(a) Fill in the missing probability value on the diagram.  \n(b) If Sandra makes two guesses, what is the probability that  \ni. she gets the first question incorrect and the second question correct?  \nii. she gets both of them correct?  \niii. she will get only one of them correct?  \n2) The events B and C are dependent","cbCaisYtH09C6bOi","https://ap.wps.com/l/cbCaisYtH09C6bOi","pdf",1261308,"English","# Using Tree Diagrams\n## Working with Tree Diagrams\n# IB Questions: Independent Events\n## Practice with Independent Events\n# Practice with Dependent Events\n## Independent vs Dependent Reasoning\n# Additional Probability Problems\n## Conditional Probability and Tables","[{\"question\":\"How do you calculate the probability of a specific outcome on a tree diagram?\",\"answer\":\"Multiply the probabilities along the branches that make up that outcome path.\"},{\"question\":\"When do you add probabilities in a tree diagram question?\",\"answer\":\"Add probabilities when the question asks for an event that occurs through more than one branch (multiple possible paths).\"},{\"question\":\"What is the difference between independent and dependent events in these lessons?\",\"answer\":\"Independent events mean one event does not affect the other, while dependent events mean the outcome of one affects the probability of the other.\"}]","Lesson 10-8 - Tree Diagrams | PDF",1792978004]