// Numbas version: finer_feedback_settings
{"name": "PB1 - Joint Probability", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "PB1 - Joint Probability", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Researchers collected observations of bee species and recorded if the bee size was tiny (t) or large (l), and whether the bee was a red-tailed bumblebee (r) or a red-shanked carder bumblebee (c).</p>\n<p>These two discrete variables were&nbsp;<strong>not&nbsp;</strong>independent.</p>\n<p>This data was used to make this joint probability table:</p>\n<table style=\"width: 769px;\">\n<tbody>\n<tr>\n<td style=\"width: 224.812px;\"></td>\n<td style=\"width: 222.953px;\">Bee=red-tailed bumblebee <em>(</em>$B=r$<em>)</em></td>\n<td style=\"width: 272.234px;\">Bee=red-shanked carder bumblebee <em>(</em>$B=c$<em>)</em></td>\n</tr>\n<tr>\n<td style=\"width: 224.812px;\">Size = tiny ($S=t$)</td>\n<td style=\"width: 222.953px;\">{rttext}</td>\n<td style=\"width: 272.234px;\">{cttext}</td>\n</tr>\n<tr>\n<td style=\"width: 224.812px;\">Size = large ($S=l$)</td>\n<td style=\"width: 222.953px;\">{rltext}</td>\n<td style=\"width: 272.234px;\">{cltext}</td>\n</tr>\n</tbody>\n</table>", "advice": "<p><strong>a)&nbsp;</strong>We have been asked to find the joint probability for a bee that is {jointpdfchoice}.</p>\n<p>We can read this off of the table as {notation}={jointpdftext}.</p>\n<p><strong>b)</strong> To calculate the marginal probability of the bee being {size}, we must find {sizenotation}.</p>\n<p>\\begin{align}<br/>\\var{sizenotation} &amp;= \\var{sizesumnotation} \\\\<br/>&amp;= \\var{sizeprob}.<br/>\\end{align}</p>\n<p><strong>c)</strong> To calculate the marginal probability of the bee being a {bee} bumblee, we must find {beenotation}.</p>\n<p>\\begin{align}<br/>\\var{beenotation} &amp;= \\var{beesumnotation} \\\\<br/>&amp;= \\var{beeprob}.<br/>\\end{align}</p>\n<p><strong>d)</strong> For the conditional probability we want to know what is the probability that it is a {beecond} bumblee given the bee is {sizecond}. We must find {condnotation}.</p>\n<p>\\begin{align}<br/>\\var{condnotation} &amp;= \\var{condformula} \\\\<br/>&amp;= \\frac{\\var{condnum}}{\\var{conddenom}} \\\\<br/>&amp;= \\var{condprob}.<br/>\\end{align}</p>\n<p><strong>e)&nbsp;</strong>We are asked to calculate \\var{condnotation2}.</p>\n<p>We can use our previous answer to help us calculate this conditional probability since,&nbsp;</p>\n<p>\\begin{align}<br/>\\var{condnotation2} + \\var{condnotation} &amp;= \\var{condformula} + \\var{cond2formula} \\\\<br/>&amp;= \\frac{\\var{condformula_advice}}{\\var{condformula_advice}} \\\\<br/>&amp;= 1.<br/>\\end{align}</p>\n<p>So, $\\var{condnotation2} = 1 - \\var{condnotation}$.</p>\n<p>Hence,&nbsp;</p>\n<p>\\begin{align}<br/>\\var{condnotation2} &amp;= 1 - \\var{condnotation} \\\\<br/>&amp;= 1 - \\var{condprob} \\\\<br/>&amp;= \\var{1-condprob}.<br/>\\end{align}</p>\n<p><strong>f) </strong>To demonstrate that two random variables, $B$ and $S$, are not independent, you can show that their joint probability distribution is not equal to the product of their individual (marginal) probability distributions.</p>\n<p></p>\n<p><strong><a href=\"https://sheffield.ac.uk/mash/stats-resources/probability#discrete-distributions\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></strong></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"rt": {"name": "rt", "group": "Ungrouped variables", "definition": "if(random=0,rt0,if(random=1,rt1,0))", "description": "", "templateType": "anything", "can_override": false}, "ct": {"name": "ct", "group": "Ungrouped variables", "definition": "if(random=0,ct0,if(random=1,ct1,0))", "description": "", "templateType": "anything", "can_override": false}, "rl": {"name": "rl", "group": "Ungrouped variables", "definition": "if(random=0,rl0,if(random=1,rl1,0))", "description": "", "templateType": "anything", "can_override": false}, "cl": {"name": "cl", "group": "Ungrouped variables", "definition": "if(random=0,cl0,if(random=1,cl1,0))", "description": "", "templateType": "anything", "can_override": false}, "random": {"name": "random", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "rt0": {"name": "rt0", "group": "probabilities set 0", "definition": "2/12", "description": "", "templateType": "anything", "can_override": false}, "ct0": {"name": "ct0", "group": "probabilities set 0", "definition": "3/12", "description": "", "templateType": "anything", "can_override": false}, "rl0": {"name": "rl0", "group": "probabilities set 0", "definition": "6/12", "description": "", "templateType": "anything", "can_override": false}, "cl0": {"name": "cl0", "group": "probabilities set 0", "definition": "1/12", "description": "", "templateType": "anything", "can_override": false}, "random1": {"name": "random1", "group": "Read off table - joint probability", "definition": "random(1,2,3,4)", "description": "<p>Which value are we asking the students to read off the table</p>", "templateType": "anything", "can_override": false}, "jointpdfchoice": {"name": "jointpdfchoice", "group": "Read off table - joint probability", "definition": "if(random1=1,'tiny and a red-tailed',if(random1=2,'tiny and a red-shanked carder',if(random1=3,'large and a red-tailed',if(random1=4,'large and a red-shanked carder',0))))", "description": "<p>Text for which probability we're asking the students to read off the table</p>", "templateType": "anything", "can_override": false}, "jointpdf": {"name": "jointpdf", "group": "Read off table - joint probability", "definition": "if(random1=1,rt,if(random1=2,ct,if(random1=3,rl,if(random1=4,cl,0))))", "description": "<p>joint probability&nbsp;</p>", "templateType": "anything", "can_override": false}, "notation": {"name": "notation", "group": "Read off table - joint probability", "definition": "if(random1=1,'$P(S=t, B=r)$',if(random1=2,'$P(S=t, B=c)$',if(random1=3,'$P(S=l, B=r)$',if(random1=4,'$P(S=l, B=c)$',0))))", "description": "<p>Notation for selected joint probability&nbsp;</p>", "templateType": "anything", "can_override": false}, "random2": {"name": "random2", "group": "marginal probability", "definition": "random(0,0,1,1)", "description": "<p>Random number to decide whicih size we want the marginal probability for</p>", "templateType": "anything", "can_override": false}, "size": {"name": "size", "group": "marginal probability", "definition": "if(random2=0,'tiny',if(random2=1,'large',0))", "description": "<p>text for which size we want the marginal probability for&nbsp;</p>", "templateType": "anything", "can_override": false}, "sizeprob": {"name": "sizeprob", "group": "marginal probability", "definition": "if(random2=0,rt+ct,if(random2=1,rl+cl,0))", "description": "<p>marginal probability for sleected bee size</p>", "templateType": "anything", "can_override": false}, "sizenotation": {"name": "sizenotation", "group": "marginal probability", "definition": "if(random2=0,'$P(S=t)$',if(random2=1,'$P(S=l)$',0))", "description": "<p>mathematical notation for marginal probability of selected bee size</p>", "templateType": "anything", "can_override": false}, "bee": {"name": "bee", "group": "marginal probability", "definition": "if(random2=0,'red-tailed',if(random2=1,'red-shanked carder',0))", "description": "<p>The bee type we want the marginal probability for</p>", "templateType": "anything", "can_override": false}, "beeprob": {"name": "beeprob", "group": "marginal probability", "definition": "if(random2=0,rt+rl,if(random2=1,ct+cl,0))", "description": "<p>The marginal probability of the selected bee type</p>", "templateType": "anything", "can_override": false}, "beenotation": {"name": "beenotation", "group": "marginal probability", "definition": "if(random2=0,'$P(B=r)$',if(random2=1,'$P(B=c)$',0))", "description": "<p>The notation for the marginal probaility of the selected bee type</p>", "templateType": "anything", "can_override": false}, "rttext0": {"name": "rttext0", "group": "probabilities set 0", "definition": "\"<p>$\\\\frac{2}{12}$</p>\"", "description": "<p>text for table</p>", "templateType": "long string", "can_override": false}, "cttext0": {"name": "cttext0", "group": "probabilities set 0", "definition": "\"<p>$\\\\frac{3}{12}$</p>\"", "description": "<p>text for table</p>", "templateType": "long string", "can_override": false}, "rltext0": {"name": "rltext0", "group": "probabilities set 0", "definition": "\"<p>$\\\\frac{6}{12}$</p>\"", "description": "<p>text for table</p>", "templateType": "long string", "can_override": false}, "cltext0": {"name": "cltext0", "group": "probabilities set 0", "definition": "\"<p>$\\\\frac{1}{12}$</p>\"", "description": "<p>text for table</p>", "templateType": "long string", "can_override": false}, "cttext": {"name": "cttext", "group": "Ungrouped variables", "definition": "if(random=0,cttext0,if(random=1,cttext1,0))", "description": "", "templateType": "anything", "can_override": false}, "rttext": {"name": "rttext", "group": "Ungrouped variables", "definition": "if(random=0,rttext0,if(random=1,rttext1,0))", "description": "<p>text for table</p>", "templateType": "anything", "can_override": false}, "cltext": {"name": "cltext", "group": "Ungrouped variables", "definition": "if(random=0,cltext0,if(random=1,cltext1,0))", "description": "<p>text for table</p>", "templateType": "anything", "can_override": false}, "rltext": {"name": "rltext", "group": "Ungrouped variables", "definition": "if(random=0,rltext0,if(random=1,rltext1,0))", "description": "<p>text for table</p>", "templateType": "anything", "can_override": false}, "random3a": {"name": "random3a", "group": "Conditional Probability", "definition": "random(0,0,1,1)", "description": "", "templateType": "anything", "can_override": false}, "sizecond": {"name": "sizecond", "group": "Conditional Probability", "definition": "if(random3a=0, 'tiny',if(random3a=1,'large',0))", "description": "<p>size of bee for conditional probability</p>", "templateType": "anything", "can_override": false}, "beecond": {"name": "beecond", "group": "Conditional Probability", "definition": "if(random3b=1, 'red-tailed', if(random3b=0, 'red-shanked carder',0))", "description": "<p>bee type for conditional probability</p>", "templateType": "anything", "can_override": false}, "random3b": {"name": "random3b", "group": "Conditional Probability", "definition": "random(0,0,1,1)", "description": "", "templateType": "anything", "can_override": false}, "condnotation": {"name": "condnotation", "group": "Conditional Probability", "definition": "if(random3a=0 and random3b=0, '$P(B=c|S=t)$',if(random3a=1 and random3b=0, '$P(B=c|S=l)$',if(random3a=0 and random3b=1, '$P(B=r|S=t)$',if(random3a=1 and random3b=1, '$P(B=r|S=l)$',0))))", "description": "<p>mathematical notation for selected conditional probability</p>", "templateType": "anything", "can_override": false}, "condprob": {"name": "condprob", "group": "Conditional Probability", "definition": "if(random3a=0 and random3b=0, ct/(rt+ct), if(random3a=1 and random3b=0, cl/(rl+cl), if(random3a=0 and random3b=1, rt/(rt+ct), if(random3a=1 and random3b=1, rl/(rl+cl),0))))", "description": "<p>calculated condition probability for sleected bee size and type</p>", "templateType": "anything", "can_override": false}, "condnotation2": {"name": "condnotation2", "group": "Conditional Probability", "definition": "if(random3a=0 and random3b=0, '$P(B=r|S=t)$',if(random3a=1 and random3b=0, '$P(B=r|S=l)$',if(random3a=0 and random3b=1, '$P(B=c|S=t)$',if(random3a=1 and random3b=1, '$P(B=c|S=l)$',0))))", "description": "<p>Complimentary conditional probability notation so we can check they sum to one</p>", "templateType": "anything", "can_override": false}, "rt1": {"name": "rt1", "group": "probabilities set 1", "definition": "3/18", "description": "<p>joint probability</p>", "templateType": "anything", "can_override": false}, "ct1": {"name": "ct1", "group": "probabilities set 1", "definition": "5/18", "description": "<p>joint probability</p>", "templateType": "anything", "can_override": false}, "rl1": {"name": "rl1", "group": "probabilities set 1", "definition": "4/18", "description": "<p>joint probability</p>", "templateType": "anything", "can_override": false}, "cl1": {"name": "cl1", "group": "probabilities set 1", "definition": "6/18", "description": "<p>joint probability</p>", "templateType": "anything", "can_override": false}, "rttext1": {"name": "rttext1", "group": "probabilities set 1", "definition": "\"<p>$\\\\frac{3}{18}$</p>\"", "description": "<p>text for table</p>", "templateType": "long string", "can_override": false}, "cttext1": {"name": "cttext1", "group": "probabilities set 1", "definition": "\"<p>$\\\\frac{5}{18}$</p>\"", "description": "<p>text for table</p>", "templateType": "long string", "can_override": false}, "rltext1": {"name": "rltext1", "group": "probabilities set 1", "definition": "safe(\"<p>$\\\\frac{4}{18}$</p>\")", "description": "<p>text for table</p>", "templateType": "long string", "can_override": false}, "cltext1": {"name": "cltext1", "group": "probabilities set 1", "definition": "\"<p>$\\\\frac{6}{18}$</p>\"", "description": "<p>text for table</p>", "templateType": "long string", "can_override": false}, "jointpdftext": {"name": "jointpdftext", "group": "Read off table - joint probability", "definition": "if(random1=1,rttext,if(random1=2,cttext,if(random1=3,rltext,if(random1=4,cltext,0))))", "description": "", "templateType": "anything", "can_override": false}, "sizesumnotation": {"name": "sizesumnotation", "group": "marginal probability", "definition": "if(random2=0,'$P(S=t,B=r)+P(S=t,B=c)$',if(random2=1,'$P(S=l,B=r)+P(S=l,B=c)$',0))", "description": "", "templateType": "anything", "can_override": false}, "beesumnotation": {"name": "beesumnotation", "group": "marginal probability", "definition": "if(random2=0,'$P(S=t,B=r)+P(S=l,B=r)$',if(random2=1,'$P(S=t,B=c)+P(S=l,B=c)$',0))", "description": "", "templateType": "anything", "can_override": false}, "condformula": {"name": "condformula", "group": "Conditional Probability", "definition": "if(random3a=0 and random3b=0, '$P(B=c,S=t)/P(S=t)$',if(random3a=1 and random3b=0, '$P(B=c,S=l)/P(S=l)$',if(random3a=0 and random3b=1, '$P(B=r,S=t)/P(S=t)$',if(random3a=1 and random3b=1, '$P(B=r,S=l)/P(S=l)$',0))))", "description": "", "templateType": "anything", "can_override": false}, "condnum": {"name": "condnum", "group": "Conditional Probability", "definition": "if(random3a=0 and random3b=0, ct, if(random3a=1 and random3b=0, cl, if(random3a=0 and random3b=1, rt, if(random3a=1 and random3b=1, rl,0))))", "description": "", "templateType": "anything", "can_override": false}, "conddenom": {"name": "conddenom", "group": "Conditional Probability", "definition": "if(random3a=0, rt+ct, if(random3a=1, rl+cl, 0))", "description": "", "templateType": "anything", "can_override": false}, "cond2formula": {"name": "cond2formula", "group": "Conditional Probability", "definition": "if(random3a=0 and random3b=0, '$P(B=r|S=t)/P(S=t)$',if(random3a=1 and random3b=0, '$P(B=r|S=l)/P(S=l)$',if(random3a=0 and random3b=1, '$P(B=c|S=t)/P(S=t)$',if(random3a=1 and random3b=1, '$P(B=c|S=l)/P(S=l)$',0))))", "description": "", "templateType": "anything", "can_override": false}, "condformula_advice": {"name": "condformula_advice", "group": "Conditional Probability", "definition": "if(random3a=0, '$P(S=t)$', if(random3a=1, '$P(S=l)$', 0))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["rt", "ct", "rl", "cl", "random", "cttext", "rttext", "cltext", "rltext"], "variable_groups": [{"name": "probabilities set 0", "variables": ["rt0", "rttext0", "ct0", "cttext0", "rl0", "rltext0", "cl0", "cltext0"]}, {"name": "Read off table - joint probability", "variables": ["random1", "jointpdfchoice", "jointpdf", "notation", "jointpdftext"]}, {"name": "marginal probability", "variables": ["random2", "size", "sizeprob", "sizenotation", "sizesumnotation", "bee", "beeprob", "beenotation", "beesumnotation"]}, {"name": "Conditional Probability", "variables": ["random3a", "random3b", "sizecond", "beecond", "condnotation", "condformula", "condnotation2", "cond2formula", "condprob", "condnum", "conddenom", "condformula_advice"]}, {"name": "probabilities set 1", "variables": ["rt1", "ct1", "rl1", "cl1", "rttext1", "cttext1", "rltext1", "cltext1"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "a)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Reading off the table, what is the joint probability of the bee being {jointpdfchoice}, i.e., {notation}.</p>", "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "Fraction", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "jointpdf", "maxValue": "jointpdf", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "jointpdf", "maxValue": "jointpdf", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the marginal probability of the bee being {size}, i.e., {sizenotation}?</p>", "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "Fraction", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "sizeprob", "maxValue": "sizeprob", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "sizeprob", "maxValue": "sizeprob", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "c)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the marginal probability of the bee being a {bee} bumblee, i.e., {beenotation}?</p>", "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "Fraction", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "beeprob", "maxValue": "beeprob", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "beeprob", "maxValue": "beeprob", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "d)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Conditional probability: given the bee is {sizecond}, what is the probability that it is a {beecond} bumblee, i.e., {condnotation}?</p>", "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "Fraction", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", 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"extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is {condnotation2}?</p>\n<p>(You could check that {condnotation} and {condnotation2} sum to one).</p>", "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "Fraction", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "1-condprob", "maxValue": "1-condprob", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "1-condprob", "maxValue": 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