[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-362641-105":59,"doc-detail-362641-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","independent-vs-dependent-events","Independent vs. Dependent Events","","Practice worksheet distinguishing independent and dependent events through real-life and probability scenarios. Items include drawing cards with and without replacement, rolling dice, spinning and drawing marbles, selecting objects from separate containers, and everyday choices like shirts and pants. Learners decide whether the second event is affected by the first, identify independent cases from options, and explain why replacement restores independence. An answer key provides correct classifications and sample responses.",{"@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/independent-vs-dependent-events/362641/",{"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-vs-dependent-events/362641.png","ImageObject",300,407,{"name":92,"@type":93},"Franzy","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What makes two events independent?","Question",{"text":112,"@type":113},"Two events are independent when the outcome of the first event does not affect the outcome of the second event—commonly achieved by replacing an item between events.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do dependent events differ from independent events?",{"text":117,"@type":113},"Dependent events are affected by what happens first, usually when items are not replaced, so the second outcome changes based on the first.",{"name":119,"@type":110,"acceptedAnswer":120},"Why does replacing an item between events make events independent?",{"text":121,"@type":113},"Replacing resets the number and type of items, so the second draw or choice is not influenced by the first event.","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},362641,1790672907,{"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":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"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":39,"preview_page_count":4},2336478945519,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Name:    \nIndependent vs. Dependent Events  \n\n| Type of Event | What It Means |\n| --- | --- |\n| Independent | One event does not affect the outcome of the other. |\n| Dependent | One event does affect the outcome of the other (usually when items are not replaced) . |\n\nDirections: Read each situation carefully and decide if the events are independent or dependent. Circle your answer or write it in the blank.  \n1. You draw a card from a deck, then draw another card without putting the first one back. Are these events independent or dependent?  \nAnswer:    \n2. A student rolls two dice at the same time to play a game.  \nAre these events independent or dependent? Answer:    \n3. Avery spins a spinner, then pulls a marble from a bag.  \nAre the events independent or dependent? Answer:    \n4. Two different students each pick a pencil from separate cups.  \nAre the events independent or dependent?  \nAnswer:  \n___________________  \n5. A card is drawn, placed back, and then another card is drawn.  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 1  \nAre these events independent or dependent? Answer:    \n6. Which of the following situations describes independent events?  \nA. Picking two socks from a drawer without replacing  \nB. Tossing a coin and rolling a die  \nC. Choosing a marble, keeping it, and choosing again  \nAnswer:    \n7. Leah randomly selects a shirt, then picks a pair of pants from her closet.  \nAre these events independent or dependent?  \nAnswer:  \n___________________  \n8. Caleb removes a jellybean from ajar and eats it. Then he grabs another.  \nAre the two events independent or dependent?  \nAnswer:  \n___________________  \n9. In your own words, explain why replacing an item between events makes the events independent.  \n10. Give an example of a dependent event involving school supplies.  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 2  \nAnswer Key  \n1. Dependent  \n2. Independent  \n3. Independent  \n4. Independent  \n5. Independent  \n6. B  \n7. Independent  \n8. Dependent  \n9. Sample answer: When you replace an item, it resets the total number of items, so the second event isn’t affected by the first.  \n10. Sample answer: Taking a marker from a supply bin and not putting it back before another student picks one.  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 3","cbCaieLgxPstxvSX","https://ap.wps.com/l/cbCaieLgxPstxvSX","pdf",720259,"English","# Directions\n# Questions (1-10)\n## Independent vs. Dependent Scenarios\n## Explanation and Examples","[{\"question\":\"What makes two events independent?\",\"answer\":\"Two events are independent when the outcome of the first event does not affect the outcome of the second event—commonly achieved by replacing an item between events.\"},{\"question\":\"How do dependent events differ from independent events?\",\"answer\":\"Dependent events are affected by what happens first, usually when items are not replaced, so the second outcome changes based on the first.\"},{\"question\":\"Why does replacing an item between events make events independent?\",\"answer\":\"Replacing resets the number and type of items, so the second draw or choice is not influenced by the first event.\"}]","Independent vs. Dependent Events | PDF",1790148658]