// Numbas version: finer_feedback_settings
{"name": "Link Probabilities", "extensions": [], "custom_part_types": [], "resources": [["question-resources/link2.png", "link2.png"], ["question-resources/link1.png", "link1.png"], ["question-resources/link5.png", "link5.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Link Probabilities", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Some short network links are given below, made up of components (a), (b), and (c). The components work independently, so if one fails the others are not affected.</p>\n<p>The probability of each component being functional is:</p>\n<ul>\n<li>Component (a): $P(A) = \\var{probA}$;</li>\n<li>Component (b): $P(B) = \\var{probB}$;</li>\n<li>Component (c): $P(C) = \\var{probC}$.</li>\n</ul>\n<p>In each part, give all decimal places that you have calculated.</p>", "advice": "<p><strong>Series:</strong></p>\n<p>The probability that the link works is $P(A \\wedge B) = P(A) \\times P(B) = \\var{probA} \\times \\var{probB} = \\simplify{{probA}*{probB}}$.</p>\n<p><strong>Parallel:</strong></p>\n<p>The probability that the link works is $P(A \\vee B) = P(A) + P(B) - P(A) \\times P(B) = \\var{probA} + \\var{probB} - \\var{probA} \\times \\var{probB} = \\simplify{{probA} + {probB} - {probA}*{probB}}$.</p>\n<p><strong>Combined:</strong></p>\n<p>The probability that the link works is $P((A \\vee B) \\wedge C) = P(A \\vee B) \\times P(C) = \\simplify{{probA} + {probB} - {probA}*{probB}} \\times \\var{probC} = \\simplify{({probA} + {probB} - {probA}*{probB})*{probC}}$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"probA": {"name": "probA", "group": "Ungrouped variables", "definition": "random([0.5,0.6,0.7,0.8,0.9])", "description": "", "templateType": "anything", "can_override": false}, "probB": {"name": "probB", "group": "Ungrouped variables", "definition": "random([0.5,0.6,0.7,0.8,0.9] except probA)", "description": "", "templateType": "anything", "can_override": false}, "probC": {"name": "probC", "group": "Ungrouped variables", "definition": "random([0.5,0.6,0.7,0.8,0.9] except [probA,probB])", "description": "", "templateType": "anything", "can_override": false}, "series": {"name": "series", "group": "Ungrouped variables", "definition": "probA*probB", "description": "", "templateType": "anything", "can_override": false}, "parallel": {"name": "parallel", "group": "Ungrouped variables", "definition": "probA + probB - probA*probB", "description": "", "templateType": "anything", "can_override": false}, "combined": {"name": "combined", "group": "Ungrouped variables", "definition": "parallel*probC", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["probA", "probB", "probC", "series", "parallel", "combined"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "Series Probability", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><img src=\"resources/question-resources/link2.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The link functions if both of (a) or (b) function. What is the probability that the network link functions?</p>", "minValue": "series", "maxValue": "series", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Parallel Probability", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><img src=\"resources/question-resources/link1.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The link functions if either of (a) or (b) function, or both. What is the probability that the network link functions?</p>", "minValue": "parallel", "maxValue": "parallel", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Combined Probability", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><img src=\"resources/question-resources/link5.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The link functions if both of (a) and (c) function, or if (b) and (c) function, or if (a) and (b) and (c) function. What is the probability that the network link functions?</p>", "minValue": "combined", "maxValue": "combined", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Alexander Corner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5328/"}], "resources": ["question-resources/link2.png", "question-resources/link1.png", "question-resources/link5.png"]}]}], "contributors": [{"name": "Alexander Corner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5328/"}]}