[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523566-105":59,"doc-detail-523566-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","independent-and-dependent-events-worksheet","Independent and Dependent Events - Worksheet","","Worksheet on independent versus dependent events in probability, featuring multiple scenarios with coins, dice, spinners, and colored marbles or fruit. Students classify each setup as independent or dependent, then compute missing probabilities using P(A), P(B), conditional probability P(A|B) or P(B|A), and joint probability P(A and B). Includes problems where events are determined directly by replacement or sequential selection, plus a section requiring final numerical probability values.",{"@graph":69,"@context":123},[70,84,106],{"@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/independent-and-dependent-events-worksheet/523566/",{"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/independent-and-dependent-events-worksheet/523566.png","ImageObject",300,407,{"name":92,"@type":93},"dawugda","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you decide whether the events are independent or dependent in these problems?","Question",{"text":113,"@type":114},"Independence depends on whether the outcome of the first event affects the probabilities of the second. In scenarios with replacement, the second pick usually stays the same distribution; without replacement, probabilities typically change.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What probability formulas are used to check independence and find missing values?",{"text":118,"@type":114},"The worksheet uses P(A), P(B), joint probability P(A and B), and conditional probability such as P(A|B) or P(B|A). Missing values are found by applying these relationships to each scenario.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the difference between P(A and B) and P(A|B) in these exercises?",{"text":122,"@type":114},"P(A and B) represents the probability both events occur. P(A|B) represents the probability of A occurring given that B has occurred, which can differ when events are dependent.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},523566,1791497899,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"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":52,"preview_page_count":4},3985747870947,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Kuta Software-Infinite Precalculus Name   \nIndependent and Dependent Events Date  Period   \nDetermine whether the scenario involves independent or dependent events.  \n1) There are eight nickels and eight dimes in your pocket. You randomly pick a coin out of your pocket and place it on a counter. Then you randomly pick another coin. Both coins are nickels.  \n3) You flip a coin twice. The first flip lands heads-up and the second flip lands tails-up.  \nFind the probability.  \n5) A bag contains three red marbles and three blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. The first marble is red and the second marble is blue.  \n7) There are seven boys and seven girls in a class. The teacher randomly selects one student to answer a question. Later, the teacher randomly selects a different student to answer another question. The first student is a boy and the second student is a girl.  \n2) A bag contains four red marbles and six blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. Both the first and second marbles are red.  \n4) You roll a fair six-sided die three times. The die shows an even number every time.  \n6) A spinner has an equal chance of landing on each of its six numbered regions. You spin twice. The first spin lands in region one and the second spin lands in region three.  \n8) A basket contains three apples, four peaches, and three pears. You randomly select and eat three pieces of fruit. The first piece of fruit is an apple and the next two pieces are peaches.  \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 and B) = ~~ ~~􀀕􀀚􀀕􀀓􀀓~~ ~~ 12) P(A) = ~~ ~~􀀚􀀔􀀓 P(not B) = ~~ ~~􀀚􀀔􀀓 P(A |B) = ~~ ~~􀀚􀀕􀀓  \nEvents A and B are independent. Find the missing probability.  \n13) P(B) = 􀀔􀀕􀀔􀀓 P(A and B) = ~~ ~~􀀖􀀛􀀖􀀓 P(A) = ? 14) P(A) = 􀀔􀀕􀀖􀀓 P(B) = 􀀚􀀕􀀓 P(A and B) = ?  \n15) P(A) = 􀀚􀀕􀀓 P(B |A) = 􀀔􀀗 P(B) = ? 16) P(A) = 􀀔􀀕􀀖􀀓 P(B) = ~~ ~~􀀚􀀔􀀓 P(B |A) = ?  \n17) P(A) = ~~ ~~􀀚􀀔􀀓 P(B) = 􀀔􀀕 P(A or B) = ? 18) P(B) = 􀀜􀀕􀀓 P(A |B) = ~~ ~~􀀚􀀕􀀓 P(A) = ?  \nFind the missing probability.  \n19) P(B) = 􀀔􀀕 P(A |B) = ~~ ~~􀀙􀀖􀀔􀀓􀀓 P(A and B) = ? 20) P(A) = 􀀜􀀕􀀓 P(A and B) = 􀀔􀀗􀀔􀀓􀀚􀀓 P(B |A) = ?  \n21) P(A) = 􀀕􀀘 P(B |A) = ~~ ~~􀀚􀀕􀀓 P(B) = ~~ ~~􀀕􀀘 P(A or B) = ?  \n22) P(A) = ~~ ~~􀀖􀀘 P(B |A) = ~~ ~~􀀔􀀘 P(A and B) = ?  \nKuta Software-Infinite Precalculus Name   \nIndependent and Dependent Events Date  Period   \nDetermine whether the scenario involves independent or dependent events.  \n1) There are eight nickels and eight dimes in your pocket. You randomly pick a coin out of your pocket and place it on a counter. Then you randomly pick another coin. Both coins are nickels.  \nDependent  \n3) You flip a coin twice. The first flip lands heads-up and the second flip lands tails-up.  \nIndependent  \nFind the probability.  \n5) A bag contains three red marbles and three blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. The first marble is red and the second marble is blue.  \n 􀀔   \n􀀗  \n􀀠 􀀓􀀑􀀕􀀘  \n7) There are seven boys and seven girls in a class. The teacher randomly selects one student to answer a question. Later, the teacher randomly selects a different student to answer another question. The first student is a boy and the second student is a  \ngirl.  \n 􀀚   \n􀀕􀀙  \n􀁼 􀀓􀀑􀀕􀀙􀀜  \n2) A bag contains four red marbles and six blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. Both the first and second marbles are red.  \nIndependent  \n4) You roll a fair six-sided die three times. The die shows an even number every time.  \nIndependent  \n6) A spinner has an equal chance of landing on each of its six numbered regions. You spin twice. The first spin lands in region one and the second spin lands in region three.  \n􀀔  \n􀀖􀀙  \n􀁼 􀀓􀀑􀀓􀀕􀀛  \n8) A basket contains three apples, four peac","cbCaia7pbBlYlQoV","https://ap.wps.com/l/cbCaia7pbBlYlQoV","pdf",28447,"English","# Independent and Dependent Events\n## Classify scenarios as independent or dependent\n## Determine missing probabilities using P(A), P(B), and conditional probability","[{\"question\":\"How do you decide whether the events are independent or dependent in these problems?\",\"answer\":\"Independence depends on whether the outcome of the first event affects the probabilities of the second. In scenarios with replacement, the second pick usually stays the same distribution; without replacement, probabilities typically change.\"},{\"question\":\"What probability formulas are used to check independence and find missing values?\",\"answer\":\"The worksheet uses P(A), P(B), joint probability P(A and B), and conditional probability such as P(A|B) or P(B|A). Missing values are found by applying these relationships to each scenario.\"},{\"question\":\"What is the difference between P(A and B) and P(A|B) in these exercises?\",\"answer\":\"P(A and B) represents the probability both events occur. P(A|B) represents the probability of A occurring given that B has occurred, which can differ when events are dependent.\"}]","Independent and Dependent Events - Worksheet | PDF",1791427026]