// Numbas version: finer_feedback_settings
{"name": "NC NA Choose the higher probability from two fractions randomised (7)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NC NA Choose the higher probability from two fractions randomised (7)", "tags": ["LANTITE"], "metadata": {"description": "<p>Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number &amp; Algebra strand. Students are given two probabilities in ratio form, and are required to select the higher probability. There are 7 different versions of this question.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>It has rained on the day of the&nbsp;{school1} Primary School swimming carnival {rainydays1} times in the past&nbsp;{years1} years.</p>\n<p>It has rained on the day of the&nbsp;{school2} Primary School swimming carnival&nbsp;{rainydays2} times in the past&nbsp;{years2} years.</p>", "advice": "<p>To work out a probability, divide the number of desirable outcomes by the total number of outcomes.</p>\n<p>In this case, the number of rainy days for&nbsp;{school1} is {rainydays1} and the total number of swimming carnival days is {years1}.</p>\n<p>$ \\frac{\\var{rainydays1}}{\\var{years1}} $ can be converted to a fraction out of 100 by multiplying top and bottom by {100/{years1}}. This gives&nbsp;$ \\frac{\\var{rainydays1/years1*100}}{100} $ which equals {rainydays1/years1} when written as a decimal.</p>\n<p>(Alternatively, using a calculator, {rainydays1} divided by {years1} = {rainydays1/years1}).&nbsp;</p>\n<p>This is the experimental probability of rain at the&nbsp;{school1} swimming carnival.</p>\n<p>To get the probability of a rainy day for {school2},&nbsp;$ \\frac{\\var{rainydays2}}{\\var{years2}} $ can be converted to a fraction out of 100 by multiplying top and bottom by {100/{years2}}. This gives&nbsp;$ \\frac{\\var{rainydays2/years2*100}}{100} $ which equals {rainydays2/years2} when written as a decimal.</p>\n<p>(Or, using a calculator, {rainydays2} divided by&nbsp;{years2} = {(rainydays2)/{years2}}).</p>\n<p>Then compare the two decimals to decide which is higher.</p>\n<div data-jme-visible=\"{rainydays1/years1}&gt;{rainydays2/years2}\">\n<p>{rainydays1/years1} is greater than&nbsp;{rainydays2/years2}.</p>\n<p>Therefore {school1} has the higher probability of rain on the day of the swimming carnival.</p>\n</div>\n<div data-jme-visible=\"{rainydays2/years2}&gt;{rainydays1/years1}\">\n<p>{rainydays2/years2} is greater than&nbsp;{rainydays1/years1}.</p>\n<p>Therefore {school2} has the higher probability of rain on the day of the swimming carnival.</p>\n</div>\n<p></p>", "rulesets": {}, "extensions": [], "variables": {"years2": {"name": "years2", "group": "Ungrouped variables", "definition": "scenario[\"years2\"]", "description": "<p>The total number of swimming carnivals held at the&nbsp;second school of the randomly chosen pair.</p>", "templateType": "anything"}, "scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n  {\\n    \\\"school1\\\": \\\"Windy Ridge\\\",\\n    \\\"rainydays1\\\": 4,\\n    \\\"years1\\\": 25,\\n    \\\"school2\\\": \\\"West Wingham\\\",\\n    \\\"rainydays2\\\": 3,\\n    \\\"years2\\\": 20\\n  },\\n  {\\n    \\\"school1\\\": \\\"East Epson\\\",\\n    \\\"rainydays1\\\": 3,\\n    \\\"years1\\\": 25,\\n    \\\"school2\\\": \\\"North Norton\\\",\\n    \\\"rainydays2\\\": 2,\\n    \\\"years2\\\": 20\\n  },\\n  {\\n  \\\"school1\\\": \\\"UpRiver\\\",\\n    \\\"rainydays1\\\": 2,\\n    \\\"years1\\\": 25,\\n    \\\"school2\\\": \\\"DownRiver\\\",\\n    \\\"rainydays2\\\": 3,\\n    \\\"years2\\\": 50\\n    },\\n  {\\n  \\\"school1\\\": \\\"South Somerset\\\",\\n    \\\"rainydays1\\\": 2,\\n    \\\"years1\\\": 25,\\n    \\\"school2\\\": \\\"Sunny Corner\\\",\\n    \\\"rainydays2\\\": 1,\\n    \\\"years2\\\": 20\\n    },\\n    {\\n  \\\"school1\\\": \\\"MountainRidge\\\",\\n    \\\"rainydays1\\\": 9,\\n    \\\"years1\\\": 50,\\n    \\\"school2\\\": \\\"GreenValley\\\",\\n    \\\"rainydays2\\\": 4,\\n    \\\"years2\\\": 20\\n    },\\n    {\\n  \\\"school1\\\": \\\"SouthBeach\\\",\\n    \\\"rainydays1\\\": 7,\\n    \\\"years1\\\": 50,\\n    \\\"school2\\\": \\\"NorthLagoon\\\",\\n    \\\"rainydays2\\\": 3,\\n    \\\"years2\\\": 20\\n    },\\n    {\\n  \\\"school1\\\": \\\"Greenville\\\",\\n    \\\"rainydays1\\\": 4,\\n    \\\"years1\\\": 25,\\n    \\\"school2\\\": \\\"Timbertown\\\",\\n    \\\"rainydays2\\\": 4,\\n    \\\"years2\\\": 20\\n    }\\n  ]\"))", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>A list of the possible different schools and their rainfall statistics.</p>", "templateType": "json"}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>One randomly chosen pair of schools</p>", "templateType": "anything"}, "rainydays2": {"name": "rainydays2", "group": "Ungrouped variables", "definition": "scenario[\"rainydays2\"]", "description": "<p>The&nbsp;number of wet swimming carnivals at the&nbsp;second school of the randomly chosen pair.</p>", "templateType": "anything"}, "rainydays1": {"name": "rainydays1", "group": "Ungrouped variables", "definition": "scenario[\"rainydays1\"]", "description": "<p>The&nbsp;number of wet swimming carnivals at the first school of the randomly chosen pair.</p>", "templateType": "anything"}, "school2": {"name": "school2", "group": "Ungrouped variables", "definition": "scenario[\"school2\"]", "description": "<p>The name of the&nbsp;second school of the randomly chosen pair.</p>", "templateType": "anything"}, "school1": {"name": "school1", "group": "Ungrouped variables", "definition": "scenario[\"school1\"]", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The name of the first school of the randomly chosen pair.</p>", "templateType": "anything"}, "years1": {"name": "years1", "group": "Ungrouped variables", "definition": "scenario[\"years1\"]", "description": "<p>The total number of swimming carnivals held at the first school of the randomly chosen pair.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "school1", "rainydays1", "years1", "school2", "rainydays2", "years2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which school has the higher probability of rain on the day of the swimming carnival, assuming that the weather follows the long term average?&nbsp;</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["{school1} Primary School", "{school2}&nbsp;Primary School", "The probability is the same for both schools.", "It is not possible to determine this based on the information given."], "matrix": ["if(rainydays1/years1>rainydays2/years2, 1, 0)", "if(rainydays1/years1<rainydays2/years2, 1, 0)", "if(rainydays1/years1=rainydays2/years2, 1, 0)", 0], "distractors": ["To find the higher probability, you need to first calculate the probability of rain for {school2} Primary School.", "To find the higher probability, you need to first calculate the probability of rain for {school2} Primary School.", "To find the higher probability, you need to first calculate the probability of rain for {school2} Primary School.", "Work out the probability of rain for {school2} Primary School and compare it to your answer to part a) above. Click the Reveal Answers button and scroll down for Advice on how to calculate probabilities."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}