// Numbas version: exam_results_page_options
{"name": "Catherine's copy of 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": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "variable_groups": [], "name": "Catherine's copy of Decide whether pairs of events are independent, ", "variables": {"notindep": {"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    ", "name": "notindep", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "m2": {"definition": "if(u < k,1,-1)", "name": "m2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "tm": {"definition": "random(9,10,11)", "name": "tm", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "pef": {"definition": "random(0.3..0.8)", "name": "pef", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "sc3": {"definition": "a[v]", "name": "sc3", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "col": {"definition": "random(\"black\",\"brown\",\"blonde\")", "name": "col", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "m1": {"definition": "if(t < k,1,-1)", "name": "m1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "pm": {"definition": "precround(pe*pf,2)", "name": "pm", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "td": {"definition": "random(\"Monday\",\"Tuesday\", \"Wednesday\",\"Thursday\",\"Friday\")", "name": "td", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "something": {"definition": "random(\"win easily\",\"scrape a draw\", \"get beat due to a disputed penalty\")", "name": "something", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "thismany": {"definition": "random(2..4)", "name": "thismany", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "k": {"definition": "length(indep)", "name": "k", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "pf": {"definition": "random(0.2..0.7#0.1)", "name": "pf", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "t": {"definition": "random(0..abs(a)-1)", "name": "t", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "mo": {"definition": "random(\"January\",\"February\", \"March\", \"April\",\"June\", \"October\",\"November\",\"December\")", "name": "mo", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "m3": {"definition": "if(v < k,1,-1)", "name": "m3", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "pc": {"definition": "random(3..20)", "name": "pc", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "v": {"definition": "random(0..abs(a)-1 except [t,u])", "name": "v", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "a": {"definition": "indep+notindep", "name": "a", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "indep": {"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    ", "name": "indep", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "mm": {"definition": "[[m1,-m1],[m2,-m2],[m3,-m3]]", "name": "mm", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "sc2": {"definition": "a[u]", "name": "sc2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "sc1": {"definition": "a[t]", "name": "sc1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "npef": {"definition": "precround(pef^2+random(0.1..0.2#0.01),2)", "name": "npef", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "abbe": {"definition": "random(\"above\",\"below\")", "name": "abbe", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "pe": {"definition": "random(0.2..0.7#0.1)", "name": "pe", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "u": {"definition": "random(0..abs(a)-1 except t)", "name": "u", "group": "Ungrouped variables", "templateType": "anything", "description": ""}}, "rulesets": {}, "extensions": [], "functions": {}, "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"], "advice": "<p>No solution provided.</p>", "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    ", "parts": [{"marks": 0, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "prompt": "<p>[[0]]</p>", "gaps": [{"maxMarks": 0, "displayType": "radiogroup", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "minMarks": 0, "variableReplacements": [], "shuffleAnswers": false, "choices": ["<strong>First Pair: </strong>{sc1}", "<strong>Second Pair: </strong> {sc2}", "<strong>Third Pair: </strong> {sc3}"], "maxAnswers": 0, "marks": 0, "layout": {"expression": "", "type": "all"}, "matrix": "mm", "answers": ["Independent", "Not independent"], "warningType": "none", "type": "m_n_x", "shuffleChoices": false, "variableReplacementStrategy": "originalfirst", "minAnswers": 0}], "variableReplacementStrategy": "originalfirst"}], "preamble": {"js": "", "css": ""}, "metadata": {"description": "<p>Independent events in probability. Choose whether given three given pairs of events are independent or not.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}]}], "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}