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Students use given counts of beads, counters, or balls to determine how many times each color should appear out of 20 trials, then compare those expectations with tally-mark results. The key provides the final “Answers” entries for each item type and includes the probability interpretation through counts for colors such as brown, purple, black, blue, white, gray, pink, and green.",{"@graph":69,"@context":114},[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/expected-and-actual-results-answer-key/479682/",{"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/expected-and-actual-results-answer-key/479682.png","ImageObject",300,407,{"name":92,"@type":93},"4398046744996","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108],{"name":109,"@type":110,"acceptedAnswer":111},"Why are there different materials like beads, counters, and balls?","Question",{"text":112,"@type":113},"Each problem uses a different type of item to represent the same idea: compare the expected counts from the given distribution to the observed outcomes from repeated draws.","Answer","https://schema.org",{"og:url":83,"og:type":116,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":118,"canonical":83},"index,follow",{"doc_id":120,"site_id":62},479682,1793126747,{"code":4,"msg":5,"data":123},{"doc_id":120,"user_id":124,"nickname":92,"user_avatar":66,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":125,"file_id":126,"file_url":127,"file_type":128,"file_size":129,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":130,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":131,"faqs":132,"seo_title":133,"seo_description":67,"update_tm":134,"read_time":39},4398046744996,"Expected and Actual Results  \nName:  \n\n| Find how many times the color was expected and how many times it happened.\u003Cbr>1) A bead was drawn and put back 20 times. Use the number of beads to work out how many times brown should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Beads \u003Cbr>Results | 1.\u003Cbr>2. | Answers |\n| --- | --- | --- |\n|  |  |  |\n|  |  |  |\n| brown 1 purple 1 black 2 \u003Cbr>Should have come up:   Actually came up:  \u003Cbr>2) A counter was drawn and put back 20 times. Use the number of counters to work out how many times blue should have come up, then count the tally marks to see how many times it did.\u003Cbr>| 3.\u003Cbr>4. |  |\n|  |  |  |\n|  |  |  |\n| white 1 blue 2 black 2 \u003Cbr>Should have come up:   Actually came up:  \u003Cbr>3) A ball was scooped from the bin and dropped back 20 times. Use the number of balls to work out how many times green should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Balls \u003Cbr>Results gray 3 pink 1 |  |  |\n| green 1\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>4) A bead was pulled from the bag and put back 20 times. Use the number of beads to work out how many times purple should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Should have come up:   Actually came up:   |  |  |\n| 9 |  | 1-4  75  50  25  0  |\n\n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \nMath  \nExpected and Actual Results  \nName: Answer Key  \n\n| Find how many times the color was expected and how many times it happened.\u003Cbr>1) A bead was drawn and put back 20 times. Use the number of beads to work out how many times brown should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Beads \u003Cbr>Results | 1.\u003Cbr>2. | Answers\u003Cbr>5, 4 |\n| --- | --- | --- |\n|  |  | 8, 7 |\n|  |  |  |\n| brown 1 purple 1 black 2 \u003Cbr>Should have come up:   Actually came up:  \u003Cbr>2) A counter was drawn and put back 20 times. Use the number of counters to work out how many times blue should have come up, then count the tally marks to see how many times it did.\u003Cbr>| 3.\u003Cbr>4. | 4, 7 |\n|  |  | 5, 2 |\n|  |  |  |\n| white 1 blue 2 black 2 \u003Cbr>Should have come up:   Actually came up:  \u003Cbr>3) A ball was scooped from the bin and dropped back 20 times. Use the number of balls to work out how many times green should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Balls \u003Cbr>Results gray 3 pink 1 |  |  |\n| green 1\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>4) A bead was pulled from the bag and put back 20 times. Use the number of beads to work out how many times purple should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Should have come up:   Actually came up:   |  |  |\n| 9 |  | 1-4  75  50  25  0  |\n\n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \nMath  \nExpected and Actual Results  \nName:  \n\n| Find how many times the color was expected and how many times it happened.\u003Cbr>1) A bead was drawn and put back 20 times. Use the number of beads to work out how many times brown should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Beads \u003Cbr>Results | 1.\u003Cbr>2. | Answers |\n| --- | --- | --- |\n|  |  |  |\n|  |  |  |\n| brown 1 purple 1 black 2 \u003Cbr>Should have come up:   Actually came up:  \u003Cbr>2) A counter was drawn and put back 20 times. Use the number of counters to work out how many times blue should have come up, then count the tally marks to see how many times it did.\u003Cbr>| 3.\u003Cbr>4. |  |\n|  |  |  |\n|  |  |  |\n| white 1 blue 2 black 2 \u003Cbr>Should have come up:   Actually came up:  \u003Cbr>3) A ball was scooped from the bin and dropped back 20 times. Use the number of balls to work out how many times green should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Balls \u003Cbr>Results gray 3 pink 1 |  |  |\n| green 1\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>4) A bead was pulled ","cbCaihUaXURkK577","https://ap.wps.com/l/cbCaihUaXURkK577","pdf",65475,"English","# Find how many times each color was expected and how many times it happened\n## Beads drawn and replaced 20 times\n## Counters drawn and replaced 20 times\n## Balls scooped and dropped 20 times\n## Beads pulled from a bag and replaced 20 times","[{\"question\":\"Why are there different materials like beads, counters, and balls?\",\"answer\":\"Each problem uses a different type of item to represent the same idea: compare the expected counts from the given distribution to the observed outcomes from repeated draws.\"}]","Expected and Actual Results - Answer Key | PDF",1790793697]