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Problems cover balls, pegs, and counters, with provided solution values for each color and trial.",{"@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/expected-and-actual-results-math-answer-key/479683/",{"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-math-answer-key/479683.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":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the worksheet ask students to compare?","Question",{"text":112,"@type":113},"It asks for the expected number of times each color should appear and the actual number of times it happens, based on tallies after 20 draws with replacement.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is “expected” determined in each problem?",{"text":117,"@type":113},"Students use the counts of each type (e.g., number of balls of each color) to calculate how many times a target color (like yellow) should appear in 20 draws.",{"name":119,"@type":110,"acceptedAnswer":120},"What happens during the draws for balls, pegs, and counters?",{"text":121,"@type":113},"Each item is drawn and then put back, repeated 20 times, so the tallies reflect the observed actual results for each color.","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},479683,1793030983,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":66,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":138,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":139,"faqs":140,"seo_title":141,"seo_description":67,"update_tm":142,"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 ball was pulled and put back 20 times. Use the number of balls to work out how many times yellow should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Balls \u003Cbr>Results | 1.\u003Cbr>2. | Answers |\n| --- | --- | --- |\n|  |  |  |\n|  |  |  |\n| white 3 red 2 yellow 5 \u003Cbr>\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>2) A peg was drawn from the bin and put back 20 times. Use the number of pegs to work out how many times yellow should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Pegs \u003Cbr>Results brown 2 yellow 1 | 3.\u003Cbr>4. |  |\n|  |  |  |\n|  |  |  |\n| white 2 \u003Cbr>\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>3) A counter was drawn from the tub and put back 20 times. Use the number of counters 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>Counters \u003Cbr>Results green 1 brown 1 |  |  |\n| gray 2 \u003Cbr>\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>4) A peg was drawn and put back 20 times. Use the number of pegs to work out how many times black should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Pegs \u003Cbr>Results green 1 yellow 2 black 1 \u003Cbr>Should have come up:   Actually came up:   |  |  |\n| 10 |  | 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 ball was pulled and put back 20 times. Use the number of balls to work out how many times yellow should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Balls \u003Cbr>Results | 1.\u003Cbr>2. | Answers\u003Cbr>10, 7 |\n| --- | --- | --- |\n|  |  | 4, 2 |\n|  |  |  |\n| white 3 red 2 yellow 5 \u003Cbr>\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>2) A peg was drawn from the bin and put back 20 times. Use the number of pegs to work out how many times yellow should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Pegs \u003Cbr>Results brown 2 yellow 1 | 3.\u003Cbr>4. | 5, 8 |\n|  |  | 5, 5 |\n|  |  |  |\n| white 2 \u003Cbr>\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>3) A counter was drawn from the tub and put back 20 times. Use the number of counters 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>Counters \u003Cbr>Results green 1 brown 1 |  |  |\n| gray 2 \u003Cbr>\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>4) A peg was drawn and put back 20 times. Use the number of pegs to work out how many times black should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Pegs \u003Cbr>Results green 1 yellow 2 black 1 \u003Cbr>Should have come up:   Actually came up:   |  |  |\n| 10 |  | 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 ball was pulled and put back 20 times. Use the number of balls to work out how many times yellow should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Balls \u003Cbr>Results | 1.\u003Cbr>2. | Answers |\n| --- | --- | --- |\n|  |  |  |\n|  |  |  |\n| white 3 red 2 yellow 5 \u003Cbr>\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>2) A peg was drawn from the bin and put back 20 times. Use the number of pegs to work out how many times yellow should have come up, then count the tally marks to see how many times it did.\u003Cbr>\u003Cbr>Color \u003Cbr>Pegs \u003Cbr>Results brown 2 yellow 1 | 3.\u003Cbr>4. |  |\n|  |  |  |\n|  |  |  |\n| white 2 \u003Cbr>\u003Cbr>Should have come up:   Actually came up:  \u003Cbr>3) A counter was drawn from the tub and put back 20 times. Use the number of counters to wo","cbCaip9TliqmfaBC","https://ap.wps.com/l/cbCaip9TliqmfaBC","pdf",64104,"English","# Expected and Actual Results\n## Balls: expected vs actual\n## Pegs: expected vs actual\n## Counters: expected vs actual\n## Pegs again: black expected vs actual","[{\"question\":\"What does the worksheet ask students to compare?\",\"answer\":\"It asks for the expected number of times each color should appear and the actual number of times it happens, based on tallies after 20 draws with replacement.\"},{\"question\":\"How is “expected” determined in each problem?\",\"answer\":\"Students use the counts of each type (e.g., number of balls of each color) to calculate how many times a target color (like yellow) should appear in 20 draws.\"},{\"question\":\"What happens during the draws for balls, pegs, and counters?\",\"answer\":\"Each item is drawn and then put back, repeated 20 times, so the tallies reflect the observed actual results for each color.\"}]","Expected and Actual Results - Math Answer Key | PDF",1790793700]