// Numbas version: exam_results_page_options
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{"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "a12+random(5..15#5)", "name": "a22"}, "maxemv": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "max(list(emv))", "name": "maxemv"}, "a01": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(40..70#10)", "name": "a01"}, "a02": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-40..-10#10)", "name": "a02"}, "p1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "precround(random(0.2..0.35#0.05),2)", "name": "p1"}, "hasdonethis": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "\"has developed a new car immobiliser \"", "name": "hasdonethis"}, "p": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "[p1,p2,p3]", "name": "p"}, "correct": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "switch(mm[0]=1,Cat[0],mm[1]=1,Cat[1],Cat[2])", "name": "correct"}, "emv": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "matrix(a)*vector(p)", "name": "emv"}, "a21": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "round(a01*random(0.7..0.85))", "name": "a21"}, "a10": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "round(random(0.75..0.9#0.5)*a00)", "name": "a10"}, "a": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "[[a00,a01,a02],[a10,a11,a12],[a20,a21,a22]]", "name": "a"}, "something": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "\"A car accessory company, Marla PLC, \"", "name": "something"}, "product": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "\"product\"", "name": "product"}, "p2": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "precround(p1+random(0.05..0.1#0.05),2)", "name": "p2"}, "expectedreturn": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "\"the Marketing Director's thoughts on the likely profit (in thousands of pounds) to be earned\"", "name": "expectedreturn"}, "att": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "[\"Outcome:\",\"highly successful\",\"moderately successful\",\"limited success/failure\"]", "name": "att"}, "p3": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "precround(1-p1-p2,2)", "name": "p3"}, "a11": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "round(random(0.75..0.95#0.5)*a01)", "name": "a11"}, "b": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "map([cat[x]]+a[x],x,0..2)", "name": "b"}, "info": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "\"Initial market research\"", "name": "info"}, "mm": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "map(award(1,maxemv=emv[x]),x,0..abs(cat)-1)", "name": "mm"}, "a00": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(80..120#10)", "name": "a00"}, "a12": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(5..15#5)", "name": "a12"}, "units": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "'thousands of pounds'", "name": "units"}}, "preamble": {"css": "", "js": ""}, "functions": {}, "extensions": ["stats"], "rulesets": {}, "parts": [{"useCustomName": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "scripts": {}, "variableReplacements": [], "gaps": [{"useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "mustBeReduced": false, "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "emv[0]", "unitTests": [], "maxValue": "emv[0]", "marks": 1, "type": "numberentry", "showFractionHint": true, "customName": "", "customMarkingAlgorithm": ""}, {"useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "mustBeReduced": false, "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "emv[1]", "unitTests": [], "maxValue": "emv[1]", "marks": 1, "type": "numberentry", "showFractionHint": true, "customName": "", "customMarkingAlgorithm": ""}, {"useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "mustBeReduced": false, "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "emv[2]", "unitTests": [], "maxValue": "emv[2]", "marks": 1, "type": "numberentry", "showFractionHint": true, "customName": "", "customMarkingAlgorithm": ""}], "showFeedbackIcon": true, "unitTests": [], "prompt": "<p>Calculate the Expected Monetary Value (EMV), in thousands of pounds, for each option:</p>\n<table>\n<tbody>\n<tr>\n<td style=\"vertical-align: middle; border-right: 1px solid;\">&nbsp;</td>\n<td style=\"vertical-align: middle; border-top: 1px solid; border-bottom: 1px solid; border-right: 1px solid;\"><strong>EMV</strong></td>\n</tr>\n<tr>\n<td style=\"vertical-align: middle; border-right: 1px solid;\"><strong>{Cat[0]}</strong></td>\n<td style=\"border-right: 1px solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"vertical-align: middle; border-right: 1px solid;\"><strong>{Cat[1]}</strong></td>\n<td style=\"vertical-align: middle; border-right: 1px solid;\">[[1]]</td>\n</tr>\n<tr>\n<td style=\"vertical-align: middle; border-right: 1px solid;\"><strong>{Cat[2]}</strong></td>\n<td style=\"border-right: 1px solid; border-bottom: 1px solid;\">[[2]]</td>\n</tr>\n</tbody>\n</table>", "marks": 0, "type": "gapfill", "customName": "", "customMarkingAlgorithm": ""}, {"useCustomName": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "shuffleChoices": false, "scripts": {}, "choices": ["<strong>{Cat[0]}</strong>", "<strong>{Cat[1]}</strong>", "<strong>{Cat[2]}</strong>"], "variableReplacements": [], "showCellAnswerState": true, "displayType": "radiogroup", "displayColumns": 0, "showFeedbackIcon": true, "maxMarks": 0, "unitTests": [], "prompt": "\n      <p>Hence determine the optimal course of action:</p>\n        <p>&nbsp;</p>\n      ", "marks": 0, "minMarks": 0, "type": "1_n_2", "matrix": "mm", "customName": "", "customMarkingAlgorithm": ""}], "name": "Simon's copy of Make decision based on expected monetary value", "variable_groups": [], "ungrouped_variables": ["a20", "a21", "a22", "a02", "a00", "a01", "outcomes", "something", "maxemv", "decision", "units", "correct", "a", "product", "a11", "a10", "a12", "b", "p2", "p3", "p1", "mm", "info", "cat", "p", "att", "emv", "expectedreturn", "hasdonethis"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Given data on probabilities of three levels of success of three options and projections of the profits that the options will accrue depending on the level of success, find the expected monetary value (EMV) for each option and choose the one with the greatest EMV.</p>"}, "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "<p>For a given option, we can find the Expected Monetary Value by:</p>\n<ul>\n<li>Multiplying the probability of each outcome by its expected profit</li>\n<li>Adding the resulting values up</li>\n</ul>\n<p></p>\n<p>e.g. the Expected Monetary Value for \"{Cat[0]}\" is given in four steps (all numbers below are in {units}):</p>\n<p>1. &nbsp;Multiplying the probability $\\var{p1}$ &nbsp;of a {Att[1]} outcome by the expected profit $\\var{a[0][0]}$, &nbsp;gives:</p>\n<p style=\"text-align: center;\">expected profit = $\\var{p1}\\times \\var{a[0][0]}= &nbsp;\\var{p1*a[0][0]}$&nbsp;</p>\n<p>&nbsp;</p>\n<p>2. &nbsp;Multiplying the probability&nbsp;$\\var{p2}$ &nbsp;of a {Att[2]} outcome&nbsp; by the expected profit, &nbsp;$\\var{a[0][1]}$ gives:</p>\n<p style=\"text-align: center;\">&nbsp;expected profit =&nbsp;<span style=\"text-align: center;\">&nbsp;</span><span style=\"text-align: center;\">$\\var{p2}\\times \\var{a[0][1]}= &nbsp;\\var{p2*a[0][1]}$ </span>&nbsp;</p>\n<p>&nbsp;</p>\n<p>3. &nbsp;&nbsp;Multiplying the probability&nbsp;$\\var{p3}$ &nbsp;of a {Att[3]} outcome&nbsp; by the expected profit, &nbsp;$\\var{a[0][2]}$ gives:</p>\n<p style=\"text-align: center;\">&nbsp;expected profit =&nbsp;&nbsp;$\\var{p3}\\times \\var{a[0][2]}= &nbsp;\\var{p3*a[0][2]}$&nbsp;</p>\n<p>4. Finally add these three together to get the Expected Monetary Value &nbsp;for the option {Cat[0]} :</p>\n<p style=\"text-align: center;\">$\\var{p1*a[0][0]}+\\var{p2*a[0][1]}-\\var{abs(p3*a[0][2])}=\\var{emv[0]}$</p>\n<p>&nbsp;</p>\n<p>You calculate in the same way for the other options - the next table gives the Expected Monetary Value for all three::</p>\n<table>\n<tbody>\n<tr>\n<td style=\"vertical-align: middle; border-right-width: 1px; border-right-style: solid; text-align: left;\">&nbsp;</td>\n<td style=\"vertical-align: middle; border-top-width: 1px; border-top-style: solid; border-bottom-width: 1px; border-bottom-style: solid; border-right-width: 1px; border-right-style: solid; text-align: left;\"><strong>EMV</strong></td>\n</tr>\n<tr>\n<td style=\"vertical-align: middle; border-right: 1px solid;\"><strong>{Cat[0]}</strong></td>\n<td style=\"border-right: 1px solid;\">{emv[0]}</td>\n</tr>\n<tr>\n<td style=\"vertical-align: middle; border-right: 1px solid;\"><strong>{Cat[1]}</strong></td>\n<td style=\"vertical-align: middle; border-right: 1px solid;\">{emv[1]}</td>\n</tr>\n<tr>\n<td style=\"vertical-align: middle; border-right: 1px solid;\"><strong>{Cat[2]}</strong></td>\n<td style=\"border-right: 1px solid; border-bottom: 1px solid;\">{emv[2]}</td>\n</tr>\n</tbody>\n</table>\n<p>The optimal course of action is take to be that which has the highest Expected Monetary Value (EMV) and this is seen to be :</p>\n<p>{Correct} with EMV &nbsp;$\\var{maxemv}$.</p>\n<p>&nbsp;</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">&nbsp;</p>", "statement": "<p>{Something} {hasdonethis} {decision}</p>\n<p>A. {Cat[0]}</p>\n<p>B. {Cat[1]}</p>\n<p>C. {Cat[2]}</p>\n<p>{info} has the following probabilities associated to the following {outcomes} for the {product}:</p>\n<p>{table([['&lt;strong&gt;Probability:&lt;/strong&gt;']+p],Att)}</p>\n<p>The next table shows {expectedreturn} for each option against these {outcomes}:</p>\n<p>{table(b,Att)}</p>", "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}