// Numbas version: exam_results_page_options
{"name": "Decide whether pairs of events are independent, ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"mm": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[[m1,-m1],[m2,-m2],[m3,-m3]]", "description": "", "name": "mm"}, "v": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..abs(a)-1 except [t,u])", "description": "", "name": "v"}, "thismany": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "name": "thismany"}, "u": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..abs(a)-1 except t)", "description": "", "name": "u"}, "m3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(v < k,1,-1)", "description": "", "name": "m3"}, "abbe": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(\"above\",\"below\")", "description": "", "name": "abbe"}, "sc3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a[v]", "description": "", "name": "sc3"}, "pc": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..20)", "description": "", "name": "pc"}, "pe": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0.2..0.7#0.1)", "description": "", "name": "pe"}, "pm": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(pe*pf,2)", "description": "", "name": "pm"}, "indep": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\n    [\"$E\\\\; \\\\textrm{and}\\\\; F$, where $P(E \\\\;\\\\textrm{and}\\\\; F) = P(E) \\\\times P(F)$.\",\n    \"$E\\\\; \\\\textrm{and}\\\\; F$, where $P(E)= \\\\var{pe}$, $P(F)= \\\\var{pf}$ and $P(E\\\\; \\\\textrm{and}\\\\; F)=\\\\var{pm}$\",\n    \"H: A new laundry detergent will capture $\\\\var{pc} of the market next year, K: Rover will produce a new model next year.\",\n    \"H: Spinning a six and K: spinning a five on the same spinner.\",\n    \"A: I look out of the window and it is sunny, B: I win the National Lottery jackpot this weekend!\",\n    \"A: I look out of the window and it is cloudy, B: Newcastle \"+{something}+\" this weekend.\",\n    \"$E\\\\; \\\\textrm{and}\\\\; F$, where $P(E)= P(F)$ and $P(E\\\\; \\\\textrm{and}\\\\; F)= P(E) \\\\times P(F)$\",\n    \"A student is selected at random from this class. The events A and B are such that A: the student has \"+ abbe+ \" average shoe size and B: the student was born in \"+ {mo},\n    \"E: An individual eats out more than \"+thismany+\" times a week. F: An individual has \"+col+\" hair.\",\n    \"$H$ and $K$, where $P(K) = P(K|H)$.\"]\n    ", "description": "", "name": "indep"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "indep+notindep", "description": "", "name": "a"}, "pef": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0.3..0.8)", "description": "", "name": "pef"}, "tm": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(9,10,11)", "description": "", "name": "tm"}, "something": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(\"win easily\",\"scrape a draw\", \"get beat due to a disputed penalty\")", "description": "", "name": "something"}, "npef": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(pef^2+random(0.1..0.2#0.01),2)", "description": "", "name": "npef"}, "m2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(u < k,1,-1)", "description": "", "name": "m2"}, "k": {"templateType": "anything", "group": "Ungrouped variables", "definition": "length(indep)", "description": "", "name": "k"}, "sc1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a[t]", "description": "", "name": "sc1"}, "m1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(t < k,1,-1)", "description": "", "name": "m1"}, "col": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(\"black\",\"brown\",\"blonde\")", "description": "", "name": "col"}, "notindep": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\n    [\"A: The sky is cloudy today. B: It will rain today.\",\n    \"A: A level marks in Mathematics, B: A level marks in Physics from students in the same school.\",\n    \"$E\\\\; \\\\textrm{and}\\\\; F$, where $P(E)= P(F)=\\\\var{pef}$ and $P(E\\\\; \\\\textrm{and}\\\\; F)= \\\\var{npef}$\",\n    \"H: Tom lies in on \"+ td + \", K: Tom is late for his \"+ tm+\" o'clock lecture on \"+ td,\n    \"A student is selected at random from this class. The events H and K are such that H: the student is \"+ abbe+ \" average in height and K: the student is \"+abbe +\" average in weight.\",\n    \"$E\\\\; \\\\textrm{and}\\\\; F$, where $P(E\\\\; \\\\textrm{and}\\\\; F)\\\\neq P(E)\\\\times P(F)$\",\n    \"H: There is a severe thunderstorm in my home town this afternoon. K: My computer crashes this afternoon.\",\n    \"A: A patient takes an abnormally long time to recover from an operation. B: The patient is elderly.\"]\n    ", "description": "", "name": "notindep"}, "td": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(\"Monday\",\"Tuesday\", \"Wednesday\",\"Thursday\",\"Friday\")", "description": "", "name": "td"}, "sc2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a[u]", "description": "", "name": "sc2"}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..abs(a)-1)", "description": "", "name": "t"}, "pf": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0.2..0.7#0.1)", "description": "", "name": "pf"}, "mo": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(\"January\",\"February\", \"March\", \"April\",\"June\", \"October\",\"November\",\"December\")", "description": "", "name": "mo"}}, "ungrouped_variables": ["something", "indep", "pc", "tm", "pf", "m3", "m2", "m1", "td", "pm", "abbe", "npef", "pe", "thismany", "sc1", "pef", "sc3", "sc2", "a", "mm", "mo", "notindep", "col", "u", "t", "v", "k"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Decide whether pairs of events are independent, ", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"layout": {"expression": ""}, "choices": ["<strong>First Pair: </strong>{sc1}", "<strong>Second Pair: </strong> {sc2}", "<strong>Third Pair: </strong> {sc3}"], "matrix": "mm", "type": "m_n_x", "maxAnswers": 0, "shuffleChoices": false, "answers": ["Independent", "Not independent"], "scripts": {}, "minMarks": 0, "minAnswers": 0, "maxMarks": 0, "shuffleAnswers": false, "showCorrectAnswer": true, "marks": 0}], "type": "gapfill", "prompt": "<p>[[0]]</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "\n    <p>Choose whether or not the following three pairs of events are independent or not.</p>\n  <p>For every wrong choice you will lose a mark. &nbsp;The minimum mark you can get is 0.</p>\n    ", "tags": ["checked2015", "MAS1403", "MAS1604"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n        \t\t<p><strong>29/12/2012:</strong></p>\n        \t\t    <p>Added sc tag as can add more pairs of events. Note that if you add more then the number of independent events in the new list has to be updated in variables m1,m2,m3.**</p>\n        \t\t    <p>The presentation of the pairs in the MCQ is not optimal! Not sure about the rather random labelling (A and B, H and K etc).</p>\n        \t\t    <p>No solution given. Perhaps a general statement on independence in Advice or in Show steps. &nbsp;</p>\n        \t\t    <p>** Split up into two arrays, independent and not independent pairs. &nbsp;If you add events to these arrays then everything is automatically updated.</p>\n        \t\t    <p>Question tested, OK.</p>\n        \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Independent events in probability. Choose whether given three given pairs of events are independent or not.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>No solution provided.</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}