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It extends expected value to a tetrahedral die, a spinner with equal sectors, card drawing, and two described game and insurance scenarios.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/sec-2-5-probability-tree-diagrams-and-expected-value/657343/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/sec-2-5-probability-tree-diagrams-and-expected-value/657343.png","ImageObject",300,407,{"name":42,"@type":43},"Ezra","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How do you use a tree diagram to compute sandwich selection probabilities?","Question",{"text":62,"@type":63},"List every option in each category as branches, assume equal likelihood where stated, and multiply along the relevant paths. Sum the probabilities of all paths that match the condition (e.g., white bread with specific cheese/meat).","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is the difference between empirical and theoretical expected value?",{"text":67,"@type":63},"Empirical expected value is approximated by averaging observed outcomes from repeated trials. Theoretical expected value is computed by multiplying each outcome probability by its value and summing the results.",{"name":69,"@type":60,"acceptedAnswer":70},"How do you calculate expected value for games like the $2 die game or the $4 card game?",{"text":71,"@type":63},"Compute the possible payouts and the probability of each winning event (e.g., rolling 5 or 6, drawing numbered cards or an Ace). Multiply each payout by its probability and add the results to get the expected value per game.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},657343,1793095727,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":123},1099514068035,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Sec 2. 5-Probability  \nTree Diagrams and Expected Value Name:  \nTree Diagrams  \n1.  \nCreate a tree diagram showing all possible sandwiches used to create the sandwich.  \nfrom the  \nchoices above if one of each  \ncategory is  \n2.  \nWhat is the  \nprobability you will select a sandwich with white bread?  \n3. What is the probability that a customer will select a sandwich with white bread? Explain your reasoning.  \n4. If sandwiches are randomly made where each option is equally likely in each category, what is the probability you would get a sandwich with American cheese? Explain your reasoning.  \n5. If sandwiches are randomly made where each option is equally likely in each category, what is the probability you would get a sandwich on wheat bread with ham and any cheese? Explain your reasoning.  \n6. If sandwiches are randomly made where each option is equally likely in each category, what is the probability you would get a sandwich on white bread that has either beef or turkey and has Provolone cheese? Explain your reasoning.          \n7. If sandwiches are randomly made where each option is equally likely in each category, what is the probability you would get select a sandwich with neither beef nor Muenster cheese? Explain your reasoning.  \nContent: Charles A. Dana Center at The University of Texas at Austin © SECTION 2-5  \nModified Student Worksheets: Matthew M. Winking at Phoenix High School p.24  \nAt a car manufacturing plant each option is equally likely to be selected under each category to build a car.  \nModel: Toyonda Corvic  \n| Trim Level | Exterior Color | Interior Color |\n| --- | --- | --- |\n| DX | Black | Black |\n| EX | Red | Gray |\n| Si | Blue\u003Cbr>White |  |\n\n8. Create a tree diagram showing all possible versions of the is used to create the car.  \ncar from the choices above if one of each category  \n9. If each option under each category is equally likely to be selected, what is the probability that the first car being made on a given day has a Black Exterior and a Black Interior?    \nA church group in Washington state sells pumpkins every year to raise money for the children of their town. This year’s crop, however, produced very small pumpkins. The group decided to construct a corn maze in a field and charge customers to walk through the maze.  \nCustomers can only walk forward. If the customers end up at an exit with pumpkins, they win a pumpkin. The church group asked some students to advise it on various possibilities of a customer getting a pumpkin.  \nStudents were shown a simple maze as an example.  \n10. Make a tree diagram to show the group the possible paths customers might take, entering the maze on the upper,  \nmiddle, or lower path and proceeding to an exit with or without a pumpkin (at each fork in the maze a person is  \nequally likely to take any path. Finally, find the probability of ending at each gate.  \n11. A farmer created a corn maze. He charged $10 to run through the maze. Some of the trails led to winning a cash prize of $20.  \na. Make a tree diagram to show the group the possible paths customers might take, entering the maze on the upper, middle, or lower path and proceeding to an exit with or without a pumpkin (at each fork in the maze a person is equally likely to take any path. Finally, find the probability of ending at each gate.  \nb. Determine on average expected cost or gain to each person who runs through the maze.  \nExpected Values are weighted probability or percentages. How a teacher calculates your overall grade is done the same way an expected value.  \nLet’s consider the expected value of a single standard 6-sided roll of a die.  \nEMPERICALLY: Roll a die several times and find the average value of all of the outcomes. Below is a sample of 10 rolls of a die. The more trials the closer the empirical should come to matching the theoretical expected value by the Law of Large Numbers.  \nBased on these trials the average result or approximate expected value would be: E ( A roll of a die) 􀁼 1","cbCaioeb5meYMtbj","https://ap.wps.com/l/cbCaioeb5meYMtbj","pdf",12875719,"English","# Sec 2-5 Probability\n## Tree Diagrams and Expected Value\n### Sandwich selection probabilities\n### Maze path probabilities\n### Expected value with dice, spinners, and cards\n### Expected value in games and insurance","[{\"question\":\"How do you use a tree diagram to compute sandwich selection probabilities?\",\"answer\":\"List every option in each category as branches, assume equal likelihood where stated, and multiply along the relevant paths. Sum the probabilities of all paths that match the condition (e.g., white bread with specific cheese/meat).\"},{\"question\":\"What is the difference between empirical and theoretical expected value?\",\"answer\":\"Empirical expected value is approximated by averaging observed outcomes from repeated trials. Theoretical expected value is computed by multiplying each outcome probability by its value and summing the results.\"},{\"question\":\"How do you calculate expected value for games like the $2 die game or the $4 card game?\",\"answer\":\"Compute the possible payouts and the probability of each winning event (e.g., rolling 5 or 6, drawing numbered cards or an Ace). Multiply each payout by its probability and add the results to get the expected value per game.\"}]","Sec 2-5 - Probability - Tree Diagrams and Expected Value | PDF",1792977582]