{"id":1451,"date":"2013-08-18T08:35:23","date_gmt":"2013-08-18T08:35:23","guid":{"rendered":"http:\/\/theglobalschool.net\/maths\/?page_id=1451"},"modified":"2013-08-18T08:35:23","modified_gmt":"2013-08-18T08:35:23","slug":"chanceh","status":"publish","type":"page","link":"http:\/\/maths.crusoecollege.vic.edu.au\/chanceh\/","title":{"rendered":"Chance : Level H"},"content":{"rendered":"<h1>Sample Space<\/h1>\n<ul>\n<li>Construct sample spaces for single-step experiments with equally likely outcomes <a title=\"View elaborations and additional details of ACMSP167\" href=\"http:\/\/ausvels.vcaa.vic.edu.au\/Curriculum\/ContentDescription\/ACMSP167\">(ACMSP167)<\/a><\/li>\n<li>Assign probabilities to the outcomes of events and determine probabilities for events <a title=\"View elaborations and additional details of ACMSP168\" href=\"http:\/\/ausvels.vcaa.vic.edu.au\/Curriculum\/ContentDescription\/ACMSP168\">(ACMSP168)<\/a><\/li>\n<\/ul>\n<h2>Task: First Down the Mountain<\/h2>\n<p><iframe loading=\"lazy\" title=\"First Down the Mountain\" src=\"https:\/\/player.vimeo.com\/video\/72576637?dnt=1&amp;app_id=122963\" width=\"580\" height=\"435\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p><b>Investigation Sheet A: First Down The Mountain<\/b><\/p>\n<p><b>1. The Game<\/b><\/p>\n<p>The following assumes you have run two or three races using the board and dice.<\/p>\n<ol>\n<li>Why are there only 11 climbers &#8211; from 2 to 12?<\/li>\n<li>Why does climber 7 have the furthest to travel in the race?<\/li>\n<\/ol>\n<p><b>The major challenge on this worksheet is to decide which climber(s) has the best chance of winning.<\/b><\/p>\n<p><b>2. Computer Software<\/b><\/p>\n<p>Use demonstration or automatic demonstration mode.<\/p>\n<ol>\n<li>Run 10 races &#8211; note the table of results.<\/li>\n<li>Run another set of 10 races or trials &#8211; has any pattern begun to emerge?<\/li>\n<\/ol>\n<p><b>3. Dice Possibilities and Probability<\/b><\/p>\n<ol>\n<li>Make a list of all 36 possible combinations of the two dice and the totals they give. For example\u00a0\u00a0\u00a0\u00a0 \u00a0(3,5) = total 8, (1,6) = total 7<\/li>\n<li>You will notice that a total of 7 occurs most often, with 6 different ways. From this we can say that the chances of a total of 7 are 6 out of every 36 throws, or 6\/36. This is the same as 1\/6 and we can write it shorthand as Pr(7) = 1\/6.<\/li>\n<li>Write down the probabilities or chances for each of the other totals.<\/li>\n<\/ol>\n<p><b>4. Run Many Trials<\/b><\/p>\n<ol>\n<li>Run two or three sets of 100 trials with all 11 climbers.<\/li>\n<li>Is 100 trials enough to be confident of naming the &#8216;best&#8217; climber(s)?<\/li>\n<li>Run one set of 1,000 trials and one set of 10,000 trials.<\/li>\n<li>Probability: From all your results, write down your best estimate of the long term chances of each climber. Use the % form of presenting these. For example:<\/li>\n<\/ol>\n<table border=\"1\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td>\n<p align=\"center\"><b>Total <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>2 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>3 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>4 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>5 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>6 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>7 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>8 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>9 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>10 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>11 <\/b><\/p>\n<\/td>\n<td>\n<p align=\"center\"><b>12 <\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p align=\"center\"><b>Per Cent (%) Chance <\/b><\/p>\n<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Can you say with confidence which runners have the best and least chances?<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<h1>Resources<\/h1>\n<ul>\n<li><a href=\"http:\/\/maths.crusoecollege.vic.edu.au\/wp-content\/uploads\/2013\/09\/Probability-Level-H.pdf\">Skills Practice: Level H<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Sample Space Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167) Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168) Task: First&hellip;<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"_links":{"self":[{"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/pages\/1451"}],"collection":[{"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/comments?post=1451"}],"version-history":[{"count":0,"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/pages\/1451\/revisions"}],"wp:attachment":[{"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/media?parent=1451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}