// Numbas version: exam_results_page_options
{"timing": {"timedwarning": {"message": "", "action": "none"}, "timeout": {"message": "", "action": "none"}, "allowPause": false}, "feedback": {"allowrevealanswer": true, "showanswerstate": true, "intro": "", "advicethreshold": 0, "showtotalmark": true, "showactualmark": true, "feedbackmessages": []}, "name": "ProbabilityExam", "metadata": {"description": "", "licence": "None specified"}, "showstudentname": true, "percentPass": "40", "duration": 3000, "showQuestionGroupNames": false, "navigation": {"preventleave": true, "browse": true, "showfrontpage": true, "showresultspage": "oncompletion", "reverse": true, "onleave": {"message": "", "action": "none"}, "allowregen": true}, "question_groups": [{"pickingStrategy": "all-ordered", "name": "AllQuestions", "pickQuestions": 1, "questions": [{"name": "Probability1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}, {"name": "neslihan suzen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2584/"}], "advice": "", "parts": [{"notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacements": [], "prompt": "<p>$A = \\{$ {firstval} or {secondval} appears $\\}$</p>", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "maxValue": "sol1", "scripts": {}, "extendBaseMarkingAlgorithm": true, "minValue": "sol1", "correctAnswerStyle": "plain", "type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"notationStyles": ["plain", "en", "si-en"], "allowFractions": true, "variableReplacements": [], "prompt": "<p>$C = \\{$ {oddevenstring} number appears$\\}$</p>", "correctAnswerFraction": true, "customMarkingAlgorithm": "", "maxValue": "oddevenfreq", "scripts": {}, "extendBaseMarkingAlgorithm": true, "minValue": "oddevenfreq", "correctAnswerStyle": "plain", "type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"n4": {"group": "Ungrouped variables", "templateType": "randrange", "definition": "random(14..20#1)", "description": "", "name": "n4"}, "n1": {"group": "Ungrouped variables", "templateType": "randrange", "definition": "random(14..20#1)", "description": "", "name": "n1"}, "firstval": {"group": "Ungrouped variables", "templateType": "randrange", "definition": "random(1..6#1)", "description": "", "name": "firstval"}, "oddevenfreq": {"group": "Ungrouped variables", "templateType": "anything", "definition": "if(oddeven,(n1+n3+n5)/100,(n2+n4+n6)/100)", "description": "", "name": "oddevenfreq"}, "secondval": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(secondvalset)", "description": "", "name": "secondval"}, "sol1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "(value_list[firstval-1]+value_list[secondval-1])/100", "description": "", "name": "sol1"}, "n5": {"group": "Ungrouped variables", "templateType": "randrange", "definition": "random(14..20#1)", "description": "", "name": "n5"}, "value_list": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[n1,n2,n3,n4,n5,n6]", "description": "", "name": "value_list"}, "n3": {"group": "Ungrouped variables", "templateType": "randrange", "definition": "random(14..20#1)", "description": "", "name": "n3"}, "secondvalset": {"group": "Ungrouped variables", "templateType": "anything", "definition": "list(set(1,2,3,4,5,6)-set(firstval))", "description": "", "name": "secondvalset"}, "oddeven": {"group": "Ungrouped variables", "templateType": "randrange", "definition": "random(0..1#1)", "description": "", "name": "oddeven"}, "n6": {"group": "Ungrouped variables", "templateType": "anything", "definition": "100-n1-n2-n3-n4-n5", "description": "", "name": "n6"}, "n2": {"group": "Ungrouped variables", "templateType": "randrange", "definition": "random(14..20#1)", "description": "", "name": "n2"}, "oddevenstring": {"group": "Ungrouped variables", "templateType": "anything", "definition": "if(oddeven,\"odd\",\"even\")", "description": "", "name": "oddevenstring"}}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "ungrouped_variables": ["n1", "n2", "n3", "n4", "n5", "n6", "oddeven", "oddevenstring", "oddevenfreq", "secondvalset", "firstval", "secondval", "value_list", "sol1"], "metadata": {"description": "", "licence": "None specified"}, "functions": {}, "statement": "<p>A die is tossed $100$ times and the number appearing on the upper face recorded as follows:</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td>Number</td>\n<td>$1$</td>\n<td>$2$</td>\n<td>$3$</td>\n<td>$4$</td>\n<td>$5$</td>\n<td>$6$</td>\n</tr>\n<tr>\n<td>Frequency</td>\n<td>$\\var{n1}$</td>\n<td>$\\var{n2}$</td>\n<td>$\\var{n3}$</td>\n<td>$\\var{n4}$</td>\n<td>$\\var{n5}$</td>\n<td>$\\var{n6}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Find the relative frequency of the following events:</p>", "tags": [], "type": "question"}, {"name": "Probability2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}], "advice": "", "parts": [{"prompt": "<p>Find $A\\cup B$</p>", "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "showPreview": true, "customMarkingAlgorithm": "", "failureRate": 1, "answer": "{ans1}", "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "vsetRangePoints": 5, "type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "unitTests": [], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Find $B\\cap C$</p>", "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "showPreview": true, "customMarkingAlgorithm": "", "failureRate": 1, "answer": "{ans2}", "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "vsetRangePoints": 5, "type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "unitTests": [], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Find $\\Omega\\setminus B$</p>", "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "showPreview": true, "customMarkingAlgorithm": "", "failureRate": 1, "answer": "{ans3}", "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "vsetRangePoints": 5, "type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "unitTests": [], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Find $(\\bar{A}\\cup C)\\cap B$</p>", "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "showPreview": true, "customMarkingAlgorithm": "", "failureRate": 1, "answer": "{ans4}", "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "vsetRangePoints": 5, "type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "unitTests": [], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"A": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "set(sort(shuffle(list(O))[0..5]))", "name": "A"}, "ans2": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "intersection(B,C)", "name": "ans2"}, "C": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "set(sort(shuffle(list(O))[0..3]))", "name": "C"}, "B": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "set(sort(shuffle(list(O))[0..4]))", "name": "B"}, "O": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "set(0,1,2,3,4,5,6,7,8,9,10)", "name": "O"}, "ans1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "union(A,B)", "name": "ans1"}, "ans4": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "intersection(union((O-A),C),B)", "name": "ans4"}, "ans3": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "O-B", "name": "ans3"}}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "ungrouped_variables": ["O", "A", "B", "C", "ans1", "ans2", "ans3", "ans4"], "metadata": {"description": "", "licence": "None specified"}, "functions": {}, "statement": "<p>Let $\\Omega = \\var{O}$ and $A$, $B$ and $C$ be the events:</p>\n<p>$A=\\var{A}$,&nbsp;$B=\\var{B}$,&nbsp;$C=\\var{C}$</p>", "tags": [], "type": "question"}, {"name": "Probability3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}], "advice": "", "parts": [{"prompt": "<p>Do not take mathematics</p>", "maxValue": "ans1", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "ans1", "mustBeReducedPC": 0, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Take mathematics or physics (or both)</p>", "maxValue": "ans2", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "ans2", "mustBeReducedPC": 0, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Take physics but not mathematics</p>", "maxValue": "ans3", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "ans3", "mustBeReducedPC": 0, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Take exactly one of the two subjects.</p>", "maxValue": "ans4", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "ans4", "mustBeReducedPC": 0, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Take neither mathematics nor physics.</p>", "maxValue": "ans5", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "ans5", "mustBeReducedPC": 0, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans5": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "total-(maths+physics-both)", "name": "ans5"}, "maths": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(30..total)", "name": "maths"}, "total": {"description": "", "templateType": "randrange", "group": "Ungrouped variables", "definition": "random(80..150#10)", "name": "total"}, "ans4": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "maths+physics-2*both", "name": "ans4"}, "ans2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "maths+physics-both", "name": "ans2"}, "ans1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "total-maths", "name": "ans1"}, "both": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(max(0,(maths+physics-total))..min(physics,maths))", "name": "both"}, "physics": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(20..(total-30))", "name": "physics"}, "ans3": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "physics-both", "name": "ans3"}}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "ungrouped_variables": ["total", "maths", "physics", "both", "ans1", "ans2", "ans3", "ans4", "ans5"], "metadata": {"description": "", "licence": "None specified"}, "rulesets": {}, "statement": "<p>Among {total} A-Level students in a sixth form college, {maths} take mathematics, {physics} take physics and {both} take both mathematics and physics.</p>\n<p></p>\n<p>Find the number of students who:</p>", "tags": [], "type": "question"}, {"name": "Probability4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}], "ungrouped_variables": ["sumval", "d", "appears", "appearstring", "firstsecond", "firstsecondstring", "equals", "equalstring", "ans1", "ans3", "ans2"], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Two fair, standard dice are thrown and the sum of the two faces recorded.</p>\n<p></p>\n<p>Find the probabilities of the following:</p>", "functions": {}, "rulesets": {}, "variables": {"ans2": {"description": "", "templateType": "anything", "name": "ans2", "group": "Ungrouped variables", "definition": "((14-sumval)*(12-sumval+1)/2)/36"}, "ans1": {"description": "", "templateType": "anything", "name": "ans1", "group": "Ungrouped variables", "definition": "if(equals,1/6,5/6)"}, "appearstring": {"description": "", "templateType": "anything", "name": "appearstring", "group": "Ungrouped variables", "definition": "if(appears,\"appears\",\"does not appear\")"}, "equals": {"description": "", "templateType": "randrange", "name": "equals", "group": "Ungrouped variables", "definition": "random(0..1#1)"}, "firstsecondstring": {"description": "", "templateType": "anything", "name": "firstsecondstring", "group": "Ungrouped variables", "definition": "if(firstsecond=0,\"on first die\",if(firstsecond=1,\"on second die\",\"on both dice\"))"}, "sumval": {"description": "<p>Sum is sumval or more</p>", "templateType": "randrange", "name": "sumval", "group": "Ungrouped variables", "definition": "random(7..11#1)"}, "firstsecond": {"description": "", "templateType": "randrange", "name": "firstsecond", "group": "Ungrouped variables", "definition": "random(0..2#1)"}, "ans3": {"description": "", "templateType": "anything", "name": "ans3", "group": "Ungrouped variables", "definition": "if(appears,if((firstsecond=1)||(firstsecond=0),1/6,1/36),if((firstsecond=1)||(firstsecond=0),5/6,35/36))"}, "equalstring": {"description": "", "templateType": "anything", "name": "equalstring", "group": "Ungrouped variables", "definition": "if(equals,\"equal\",\"not equal\")"}, "d": {"description": "<p>Value to appear on 1 die</p>", "templateType": "randrange", "name": "d", "group": "Ungrouped variables", "definition": "random(1..6#1)"}, "appears": {"description": "", "templateType": "randrange", "name": "appears", "group": "Ungrouped variables", "definition": "random(0..1#1)"}}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "advice": "", "parts": [{"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "prompt": "<p>$A = \\{$ two numbers are {equalstring} $\\}$</p>", "allowFractions": true, "marks": 1, "type": "numberentry", "scripts": {}, "variableReplacements": [], "showCorrectAnswer": true, "mustBeReduced": false, "correctAnswerFraction": true, "minValue": "ans1", "showFeedbackIcon": true, "maxValue": "ans1"}, {"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "prompt": "<p>$B=\\{$ sum is $\\var{sumval}$ or more $\\}$</p>", "allowFractions": true, "marks": 1, "type": "numberentry", "scripts": {}, "variableReplacements": [], "showCorrectAnswer": true, "mustBeReduced": false, "correctAnswerFraction": true, "minValue": "ans2", "showFeedbackIcon": true, "maxValue": "ans2"}, {"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "prompt": "<p>$C = \\{\\var{d}$ {appearstring} {firstsecondstring} $\\}$</p>", "allowFractions": true, "marks": 1, "type": "numberentry", "scripts": {}, "variableReplacements": [], "showCorrectAnswer": true, "mustBeReduced": false, "correctAnswerFraction": true, "minValue": "ans3", "showFeedbackIcon": true, "maxValue": "ans3"}], "metadata": {"description": "", "licence": "None specified"}, "tags": [], "type": "question"}, {"name": "Probability5", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}], "variables": {"partbn": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "n-partan", "name": "partbn"}, "partb": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "noqs-parta", "name": "partb"}, "ans2": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "combination(noqs-firstn,n-firstn)", "name": "ans2"}, "parta": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "floor(noqs/2)-1", "name": "parta"}, "partan": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(parta-2,parta-1)", "name": "partan"}, "firstn": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(3,n-2)", "name": "firstn"}, "noqs": {"description": "<p>Total number of questions</p>", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(10..15#1)", "name": "noqs"}, "ans3": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "combination(parta,partan)*combination(partb,partbn)", "name": "ans3"}, "ans1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "combination(noqs,n)", "name": "ans1"}, "n": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(noqs-5,noqs-3)", "name": "n"}}, "advice": "", "statement": "<p>A student is to answer $\\var{n}$ out of $\\var{noqs}$ questions on an exam.</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "tags": [], "variable_groups": [], "ungrouped_variables": ["noqs", "n", "firstn", "ans1", "ans2", "parta", "partb", "partan", "partbn", "ans3"], "functions": {}, "metadata": {"licence": "None specified", "description": ""}, "parts": [{"marks": 1, "type": "numberentry", "scripts": {}, "allowFractions": false, "maxValue": "ans1", "prompt": "<p>Find the number of ways $n$ the student can choose the $\\var{n}$ questions.</p>", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "minValue": "ans1", "showCorrectAnswer": true, "mustBeReduced": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false}, {"marks": 1, "type": "numberentry", "scripts": {}, "allowFractions": false, "maxValue": "ans2", "prompt": "<p>Find $n$ if the student must answer the first $\\var{firstn}$ questions.</p>", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "minValue": "ans2", "showCorrectAnswer": true, "mustBeReduced": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false}, {"marks": 1, "type": "numberentry", "scripts": {}, "allowFractions": false, "maxValue": "ans3", "prompt": "<p>Suppose the exam is divided into $2$ parts.</p>\n<ul>\n<li>Part A has $\\var{parta}$ questions;</li>\n<li>Part B has $\\var{partb}$ questions.</li>\n</ul>\n<p>If the student has to answer $\\var{partan}$ questions from Part A and $\\var{partbn}$ questions from Part B, what is $n$ in this case?</p>", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "minValue": "ans3", "showCorrectAnswer": true, "mustBeReduced": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false}], "preamble": {"css": "", "js": ""}, "type": "question"}, {"name": "Probability6", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}], "advice": "", "parts": [{"prompt": "<p>if anybody can drive;</p>", "scripts": {}, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "maxValue": "ans1", "allowFractions": false, "marks": 1, "unitTests": [], "correctAnswerStyle": "plain", "type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "ans1", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "correctAnswerFraction": false}, {"prompt": "<p>one of only $\\var{drivers}$ can drive.</p>", "scripts": {}, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "maxValue": "ans2", "allowFractions": false, "marks": 1, "unitTests": [], "correctAnswerStyle": "plain", "type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "ans2", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "correctAnswerFraction": false}], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"drivers": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..npeople-2)", "name": "drivers"}, "npeople": {"description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(4..8#1)", "name": "npeople"}, "ans2": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "drivers*factorial(npeople-1)", "name": "ans2"}, "ans1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "factorial(npeople)", "name": "ans1"}}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "ungrouped_variables": ["npeople", "drivers", "ans1", "ans2"], "metadata": {"description": "", "licence": "None specified"}, "rulesets": {}, "statement": "<p>Find the number of ways $\\var{npeople}$ people can sit in a car with $\\var{npeople}$ seats</p>", "tags": [], "type": "question"}, {"name": "Probability7", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}], "variables": {"odd": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(0,1)", "name": "odd"}, "ans1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(15-n)/15", "name": "ans1"}, "ans2": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "length(filter(x>n,x,oddset))/length(oddset)", "name": "ans2"}, "n": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(8,12)", "name": "n"}, "oddset": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "if(odd,list(1..15#2),list(2..15#2))", "name": "oddset"}, "oddstring": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "if(odd,\"odd\",\"even\")", "name": "oddstring"}}, "advice": "", "statement": "<p>A pool ball is drawn at random from a box containing $15$ pool balls numbered $1$ to $15$ and the number $n$ is recorded</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "variable_groups": [], "ungrouped_variables": ["n", "odd", "oddstring", "ans1", "ans2", "oddset"], "functions": {}, "metadata": {"licence": "None specified", "description": ""}, "parts": [{"marks": 1, "type": "numberentry", "scripts": {}, "allowFractions": true, "maxValue": "ans1", "prompt": "<p>Find the probability $p$ that $n$ exceeds $\\var{n}$.</p>", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "minValue": "ans1", "showCorrectAnswer": true, "mustBeReduced": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true}, {"marks": 1, "type": "numberentry", "scripts": {}, "allowFractions": true, "maxValue": "ans2", "prompt": "<p>If $n$ is {oddstring}, find the probability $p$ that $n$ exceeds $\\var{n}$.</p>", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "minValue": "ans2", "showCorrectAnswer": true, "mustBeReduced": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true}], "tags": [], "preamble": {"css": "", "js": ""}, "type": "question"}, {"name": "Probability8", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}], "advice": "", "tags": [], "functions": {}, "metadata": {"description": "", "licence": "None specified"}, "ungrouped_variables": ["fail_lin", "fail_calc", "fail_both", "ans1", "ans2", "ans3"], "statement": "<p>In a University, $\\var{fail_calc}\\%$ of students failed Calculus, $\\var{fail_lin}\\%$ of students failed Linear Algebra and $\\var{fail_both}\\%$ failed both Calculus and Linear Algebra. A student is selected at random.</p>", "variable_groups": [], "preamble": {"js": "", "css": ""}, "rulesets": {}, "variables": {"fail_calc": {"name": "fail_calc", "description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(10..25#5)"}, "ans2": {"name": "ans2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(fail_calc-fail_both)/fail_calc"}, "fail_lin": {"name": "fail_lin", "description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(10..25#5)"}, "ans1": {"name": "ans1", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "fail_both/fail_lin"}, "ans3": {"name": "ans3", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(100-(fail_lin+fail_calc-fail_both))/100"}, "fail_both": {"name": "fail_both", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(list(5..min(fail_lin,fail_calc)-5#5))"}}, "parts": [{"type": "numberentry", "showCorrectAnswer": true, "correctAnswerFraction": true, "prompt": "<p>If the student failed Linear Algebra, what is the probability that they failed Calculus?</p>", "variableReplacementStrategy": "originalfirst", "allowFractions": true, "minValue": "ans1", "scripts": {}, "maxValue": "ans1", "correctAnswerStyle": "plain", "mustBeReduced": false, "marks": 1, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0}, {"type": "numberentry", "showCorrectAnswer": true, "correctAnswerFraction": true, "prompt": "<p>If the student failed Calculus, what is the probability that they didn't fail Linear Algebra?</p>", "variableReplacementStrategy": "originalfirst", "allowFractions": true, "minValue": "ans2", "scripts": {}, "maxValue": "ans2", "correctAnswerStyle": "plain", "mustBeReduced": false, "marks": 1, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0}, {"type": "numberentry", "showCorrectAnswer": true, "correctAnswerFraction": true, "prompt": "<p>What is the probability that the student failed neither Calculus nor Linear Algebra?</p>", "variableReplacementStrategy": "originalfirst", "allowFractions": true, "minValue": "ans3", "scripts": {}, "maxValue": "ans3", "correctAnswerStyle": "plain", "mustBeReduced": false, "marks": 1, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question"}, {"name": "Probability9", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}], "advice": "", "functions": {}, "tags": [], "parts": [{"showFeedbackIcon": true, "allowFractions": false, "variableReplacements": [], "precisionType": "sigfig", "type": "numberentry", "minValue": "ans1", "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "maxValue": "ans1", "showCorrectAnswer": true, "showPrecisionHint": true, "correctAnswerFraction": false, "precisionPartialCredit": 0, "precision": "4", "marks": 1, "scripts": {}, "prompt": "<p>Find the probability that the item is defective.</p>", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "strictPrecision": false}, {"showFeedbackIcon": true, "allowFractions": false, "variableReplacements": [], "precisionType": "sigfig", "type": "numberentry", "minValue": "ans2", "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "maxValue": "ans2", "showCorrectAnswer": true, "showPrecisionHint": true, "correctAnswerFraction": false, "precisionPartialCredit": 0, "precision": "4", "marks": 1, "scripts": {}, "prompt": "<p>If the item is defective, find the probability that the item was produced by machine {machine}</p>", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "strictPrecision": false}], "variables": {"ans2": {"description": "", "definition": "if(machinelogical=0,percentA*A/ans1,if(machinelogical=1,percentB*B/ans1,percentC*C/ans1))/10000", "name": "ans2", "templateType": "anything", "group": "Ungrouped variables"}, "percentA": {"description": "", "definition": "random(1..5#1)", "name": "percentA", "templateType": "randrange", "group": "Ungrouped variables"}, "percentB": {"description": "", "definition": "random(2..6#1)", "name": "percentB", "templateType": "randrange", "group": "Ungrouped variables"}, "percentC": {"description": "", "definition": "random(3..7#1)", "name": "percentC", "templateType": "randrange", "group": "Ungrouped variables"}, "B": {"description": "", "definition": "random(30..50#5)", "name": "B", "templateType": "randrange", "group": "Ungrouped variables"}, "ans1": {"description": "", "definition": "(A*percentA+B*percentB+C*percentC)/10000", "name": "ans1", "templateType": "anything", "group": "Ungrouped variables"}, "machinelogical": {"description": "", "definition": "random(0..2#1)", "name": "machinelogical", "templateType": "randrange", "group": "Ungrouped variables"}, "C": {"description": "", "definition": "100-B-A", "name": "C", "templateType": "anything", "group": "Ungrouped variables"}, "machine": {"description": "", "definition": "if(machinelogical=0,\"A\",if(machinelogical=1,\"B\",if(machinelogical=2,\"C\")))", "name": "machine", "templateType": "anything", "group": "Ungrouped variables"}, "A": {"description": "", "definition": "random(20..40#5)", "name": "A", "templateType": "randrange", "group": "Ungrouped variables"}}, "statement": "<p>Three machines $A$, $B$ and $C$ produce, respectively, $\\var{A}\\%$, $\\var{B}\\%$ and $\\var{C}\\%$ of the items in a factory. The percentage of defective items produced by the machines is, respectively, $\\var{percentA}\\%$,&nbsp;$\\var{percentB}\\%$ and&nbsp;$\\var{percentC}\\%$. An item from the factory is selected at random.</p>", "variable_groups": [], "rulesets": {}, "ungrouped_variables": ["A", "B", "C", "percentA", "percentB", "percentC", "machinelogical", "machine", "ans1", "ans2"], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "None specified", "description": ""}, "type": "question"}, {"name": "Probability10", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}, {"name": "Bo Wang", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2742/"}], "rulesets": {}, "functions": {}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["M", "N", "bluered", "blueredstring", "p", "nopicked", "fewer", "fewerstring", "noballs", "ans1", "ans2", "ans3", "ans4"], "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "", "tags": [], "variables": {"N": {"templateType": "randrange", "definition": "random(3 .. 8#1)", "description": "<p>Number blue balls</p>", "name": "N", "group": "Ungrouped variables"}, "ans2": {"templateType": "anything", "definition": "nopicked*p", "description": "", "name": "ans2", "group": "Ungrouped variables"}, "ans3": {"templateType": "anything", "definition": "nopicked*p*(1-p)", "description": "", "name": "ans3", "group": "Ungrouped variables"}, "noballs": {"templateType": "randrange", "definition": "random(1 .. 4#1)", "description": "<p>no red/blue balls picked</p>", "name": "noballs", "group": "Ungrouped variables"}, "M": {"templateType": "randrange", "definition": "random(5 .. 10#1)", "description": "<p>Number of red balls</p>", "name": "M", "group": "Ungrouped variables"}, "nopicked": {"templateType": "randrange", "definition": "random(5 .. 9#1)", "description": "<p>Number of balls selected</p>", "name": "nopicked", "group": "Ungrouped variables"}, "ans4": {"templateType": "anything", "definition": "sqrt(precround(ans3,5))", "description": "", "name": "ans4", "group": "Ungrouped variables"}, "fewer": {"templateType": "randrange", "definition": "random(0 .. 1#1)", "description": "", "name": "fewer", "group": "Ungrouped variables"}, "fewerstring": {"templateType": "anything", "definition": "if(fewer,\"fewer than\",\"more than\")", "description": "", "name": "fewerstring", "group": "Ungrouped variables"}, "p": {"templateType": "anything", "definition": "if(bluered,N/(N+M),M/(N+M))", "description": "", "name": "p", "group": "Ungrouped variables"}, "blueredstring": {"templateType": "anything", "definition": "if(bluered,\"blue\",\"red\")", "description": "", "name": "blueredstring", "group": "Ungrouped variables"}, "ans1": {"templateType": "anything", "definition": "if(fewer,binomialcdf(noballs,nopicked,p),1-binomialcdf(noballs,nopicked,p))", "description": "", "name": "ans1", "group": "Ungrouped variables"}, "bluered": {"templateType": "randrange", "definition": "random(0 .. 1#1)", "description": "", "name": "bluered", "group": "Ungrouped variables"}}, "statement": "<p>A bag contains $\\var{M}$ red balls and $\\var{N}$ blue balls. A ball is selected at random from the bag, its colour noted, and it is replaced. This is performed $\\var{nopicked}$ times.</p>", "parts": [{"correctAnswerStyle": "plain", "marks": 1, "variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "type": "numberentry", "strictPrecision": false, "allowFractions": false, "showFeedbackIcon": true, "prompt": "<p>What is the probability that {fewerstring} $\\var{noballs}$ {blueredstring} balls are picked?&nbsp;</p>", "adaptiveMarkingPenalty": 0, "maxValue": "ans1", "precisionType": "dp", "variableReplacements": [], "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showPrecisionHint": true, "scripts": {}, "minValue": "ans1", "precisionMessage": "You have not given your answer to the correct precision.", "notationStyles": ["plain", "en", "si-en"], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "unitTests": [], "precision": "5", "mustBeReduced": false, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "marks": 1, "variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "type": "numberentry", "strictPrecision": false, "allowFractions": false, "showFeedbackIcon": true, "prompt": "<p>What is the expectation of the number of {blueredstring} balls selected?</p>", "adaptiveMarkingPenalty": 0, "maxValue": "ans2", "precisionType": "dp", "variableReplacements": [], "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showPrecisionHint": true, "scripts": {}, "minValue": "ans2", "precisionMessage": "You have not given your answer to the correct precision.", "notationStyles": ["plain", "en", "si-en"], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "unitTests": [], "precision": "5", "mustBeReduced": false, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "marks": 1, "variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "type": "numberentry", "strictPrecision": false, "allowFractions": false, "showFeedbackIcon": true, "prompt": "<p>What is the variance of the number of {blueredstring} balls selected?</p>", "adaptiveMarkingPenalty": 0, "maxValue": "ans3", "precisionType": "dp", "variableReplacements": [], "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showPrecisionHint": true, "scripts": {}, "minValue": "ans3", "precisionMessage": "You have not given your answer to the correct precision.", "notationStyles": ["plain", "en", "si-en"], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "unitTests": [], "precision": "5", "mustBeReduced": false, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "marks": 1, "variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "type": "numberentry", "strictPrecision": false, "allowFractions": false, "showFeedbackIcon": true, "prompt": "<p>What is the standard deviation of the number of {blueredstring} balls selected?</p>", "adaptiveMarkingPenalty": 0, "maxValue": "ans4", "precisionType": "dp", "variableReplacements": [], "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showPrecisionHint": true, "scripts": {}, "minValue": "ans4", "precisionMessage": "You have not given your answer to the correct precision.", "notationStyles": ["plain", "en", "si-en"], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "unitTests": [], "precision": "4", "mustBeReduced": false, "mustBeReducedPC": 0}], "metadata": {"licence": "None specified", "description": ""}}]}], "type": "exam", "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}], "extensions": ["stats"], "custom_part_types": [], "resources": []}