[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-523005-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-523005-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","independent-and-dependent-events","Independent and Dependent Events","","Worksheets for Infinite Geometry on independent versus dependent events and related probability calculations. Learners analyze multiple scenarios such as coin-and-die outcomes, drawing marbles with and without replacement, repeatedly drawing from a mixed cooler, and selecting fruits from a basket. The problems require identifying whether events are independent, computing joint probabilities, conditional probabilities, and missing values, including cases involving complements and event unions.",{"@graph":14,"@context":73},[15,34,56],{"@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/independent-and-dependent-events/523005/",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/independent-and-dependent-events/523005.png","ImageObject",300,407,{"name":42,"@type":43},"Đào","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-12","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you determine whether a scenario involves independent or dependent events?","Question",{"text":63,"@type":64},"The worksheet contrasts situations with replacement (independent) versus without replacement (dependent). Each listed scenario is classified accordingly.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What probability relationships are used for independent events A and B?",{"text":68,"@type":64},"For independent events, the worksheet uses the fact that A and B’s joint probability matches the product of their individual probabilities.",{"name":70,"@type":61,"acceptedAnswer":71},"What types of missing probabilities are students asked to find?",{"text":72,"@type":64},"Students solve for missing values such as P(A), P(B), P(A and B), conditional probabilities like P(B|A) or P(A|B), and also complements and unions when required.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},523005,1791496642,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},"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":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"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":55,"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,"preview_page_count":4},1374402968488,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Kuta Software-Infinite Geometry Name   \nIndependent and Dependent Events Date  Period   \nDetermine whether the scenario involves independent or dependent events.  \n1) You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows a one.  \n3) A box of chocolates contains five milk chocolates, five dark chocolates, and five white chocolates. You randomly select and eat three chocolates. The first piece is milk chocolate, the second is dark chocolate, and the third is white chocolate.  \nFind the probability.  \n5) You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows an even number.  \n7) There are eight shirts in your closet, four blue and four green. You randomly select one to wear on Monday and then a different one on Tuesday. You wear blueshirts both days.  \n2) A bag contains eight red marbles and four blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. The first marble is red and the second marble is blue.  \n4) A cooler contains ten bottles of sports drink: four lemon-lime flavored, three orange flavored, and three fruit-punch flavored. Three times, you randomly grab a bottle, return the bottle to the cooler, and then mix up the bottles. The first time, you get a lemon-lime drink. The second and third times, you get fruit-punch.  \n6) You roll a fair six-sided die twice. The first roll shows a five and the second roll shows a six.  \n8) A basket contains five apples and seven peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second piece is a peach.  \nDetermine if events A and B are independent.  \n9) P(A) = 􀀕􀀘 P(B) = ~~ ~~􀀔􀀘 P(A and B) = 􀀕􀀕􀀘~~ ~~ 10) P(A) = 􀀕􀀘 P(B) = 􀀔􀀗 P(A and B) = 􀀕􀀔􀀘  \n11) P(A) = ~~ ~~􀀜􀀕􀀓 P(B) = ~~ ~~􀀔􀀕 P(A |B) = 􀀕􀀘􀀚􀀓~~ ~~ 12) P(not A) = 􀀖􀀗 P(B) = ~~ ~~􀀖􀀔􀀓 P(A and B) = 􀀖􀀗􀀓  \nEvents A and B are independent. Find the missing probability.  \n13) P(A) = 􀀔􀀗 P(B) = ~~ ~~􀀖􀀘 P(B |A) = ? 14) P(B) = 􀀜􀀕􀀓 P(A |B) = ~~ ~~􀀔􀀘 P(A) = ?  \n15) P(A) = ~~ ~~􀀖􀀔􀀓 P(B) = 􀀔􀀕􀀖􀀓 P(A and B) = ? 16) P(B) = 􀀜􀀕􀀓 P(A and B) = ~~ ~~􀀔~~ ~~􀀜􀀓􀀓 P(A) = ?  \n17) P(A) = 􀀕􀀘 P(A and B) = ~~ ~~􀀖􀀔􀀓 P(not B) = ? 18) P(A) = ~~ ~~􀀚􀀔􀀓 P(A or B) = 􀀔􀀕􀀚􀀓􀀖􀀓 P(B) = ?  \nFind the missing probability.  \n19) P(B) = 􀀕􀀘 P(A and B) = ~~ ~~􀀔􀀔􀀓 P(A |B) = ? 20) P(A) = ~~ ~~􀀖􀀘 P(B |A) = ~~ ~~􀀖􀀔􀀓 P(A and B) = ?  \n21) P(not A) = ~~ ~~􀀖􀀘 P(A and B) = ~~ ~~􀀙􀀕􀀘 P(B |A) = ?  \n22) P(B) = 􀀓􀀑􀀗􀀘 P(A or B) = 􀀓􀀑􀀚􀀕 P(B |A) = 􀀓􀀑􀀗 P(A) = ?  \nKuta Software-Infinite Geometry Name   \nIndependent and Dependent Events Date  Period   \nDetermine whether the scenario involves independent or dependent events.  \n1) You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows a one.  \nIndependent  \n3) A box of chocolates contains five milk chocolates, five dark chocolates, and five white chocolates. You randomly select and eat three chocolates. The first piece is milk chocolate, the second is dark chocolate, and the third is white chocolate.  \nDependent  \nFind the probability.  \n5) You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows an even number.  \n 􀀔   \n􀀗  \n􀀠 􀀓􀀑􀀕􀀘  \n7) There are eight shirts in your closet, four blue and four green. You randomly select one to wear on Monday and then a different one on Tuesday. You wear blueshirts both days.  \n 􀀖   \n􀀔􀀗  \n􀁼 􀀓􀀑􀀕􀀔􀀗  \n2) A bag contains eight red marbles and four blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. The first marble is red and the second marble is blue.  \nDependent  \n4) A cooler contains ten bottles of sports drink: four lemon-lime flavored, three orange flavored, and three fruit-punch flavored. Three times, you randomly grab a bottle, return the bottle to the cooler, and then mix up the bottles. The first time, you get a lemon-lime drink. The second and third times, you","cbCailnUjGFTqYKS","https://ap.wps.com/l/cbCailnUjGFTqYKS","pdf",28639,"English","# Independent and Dependent Events\n## Determine whether scenarios involve independent or dependent events\n## Determine if events A and B are independent\n## Events A and B are independent. Find the missing probability","[{\"question\":\"How do you determine whether a scenario involves independent or dependent events?\",\"answer\":\"The worksheet contrasts situations with replacement (independent) versus without replacement (dependent). Each listed scenario is classified accordingly.\"},{\"question\":\"What probability relationships are used for independent events A and B?\",\"answer\":\"For independent events, the worksheet uses the fact that A and B’s joint probability matches the product of their individual probabilities.\"},{\"question\":\"What types of missing probabilities are students asked to find?\",\"answer\":\"Students solve for missing values such as P(A), P(B), P(A and B), conditional probabilities like P(B|A) or P(A|B), and also complements and unions when required.\"}]","Independent and Dependent Events | PDF",1791426399]