// Numbas version: finer_feedback_settings
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2) = P(X=3) + P(X=4) + P(X=5).\\\\]</p>\\n<p>\\\\[ \\\\begin{split} &amp;\\\\, P(X=3) = \\\\binom{5}{3} \\\\times \\\\var{prob}^3 \\\\times \\\\var{1-prob}^2 = \\\\var{10*prob^3*(1-prob)^2} \\\\\\\\&nbsp;&amp;\\\\, P(X=4) = \\\\binom{5}{4} \\\\times \\\\var{prob}^4 \\\\times \\\\var{1-prob} = \\\\var{5*prob^4*(1-prob)} \\\\\\\\&nbsp;&amp;\\\\,P(X=5) = \\\\binom{5}{5} \\\\times \\\\var{prob}^5 = \\\\var{prob^5} .&nbsp; \\\\end{split} \\\\]</p>\\n<p>Therefore,</p>\\n<p>\\\\[ P(X &gt; 2) = \\\\var{sol2}. \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "\"<p>If the train is delayed more than 3 times in a week, we are interested in</p>\\n<p>&nbsp;\\\\[ P(X &gt; 3) = P(X=4) + P(X=5).\\\\]</p>\\n<p>\\\\[ \\\\begin{split} &amp;\\\\, P(X=4) = \\\\binom{5}{4} \\\\times \\\\var{prob}^4 \\\\times \\\\var{1-prob} = \\\\var{5*prob^4*(1-prob)} \\\\\\\\&nbsp;&amp;\\\\,P(X=5) = \\\\binom{5}{5} \\\\times \\\\var{prob}^5 = \\\\var{prob^5} .&nbsp; \\\\end{split} \\\\]</p>\\n<p>Therefore,</p>\\n<p>\\\\[ P(X &gt; 3) = \\\\var{sol2}. \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "prob": {"name": "prob", "group": "Ungrouped variables", "definition": "n/5", "description": "", "templateType": "anything", "can_override": false}, "numd": {"name": "numd", "group": "Ungrouped variables", "definition": "random(2,3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "sol2", "sol1", "partb", "b1", "b2", "prob", "numd"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the probability that,</p>"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The commuter has no delays for a week?</p>\n<p>[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{sol1}", "maxValue": "{sol1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The train is delayed more than {numd} times in a week?</p>\n<p></p>\n<p>[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Gap 1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{sol2}", "maxValue": "{sol2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}], "resources": []}]}], "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}